Warning: This essay will contain spoilers for The Witcher 3: Wild Hunt and some references to The Witcher novels.
Part I available to read here
Part II available to read here
Part III available to read here
What the situation is in the Third Nilfgaard war is not made clear to us in the game and that's not necessarily a bad thing. While military historians amongst us would love to know each and every little pivot and engagement, the fact is that the less we know, the more we can't pick it apart at the implausibilities. However, that doesn't mean we can't speculate as to what happened and I think the game gives us a rough generality of how the war turned into a complete disaster for Nilfgaard...or a great victory.
I hope future books and supplements by CD Projekt Red will give us an idea of how the war went and what specific events occurred.
The Beginning of the War
My general idea is that Nilfgaard moved itself through Cintra and up into the North into Pontar and Lyria, which is something that wasn't going to meet them with much resistance. I hesitate at saying no resistance whatsoever because while worn down by engaging Saskia/Henselt's army, having a fully mobilized and armed military force is not going to be an easy thing to deal with either.
Still, depending on events, Saskia may be dead or missing and Henselt dead as well, leaving both forces demoralized completely. I'm going to state that the Roche path and Henselt death is the most likely outcome both with Geralt's personality as well as role-playing--Geralt might not be a political assassin but he wouldn't stop Roche from murdering him either, nor does he balk at putting down royals for personal reasons.
Another advantage the Nilfgaard possess is the support of Baroness La Vallette as well as access to the White Bridge. While her castle may or may not be burned down, the Baroness was offered sanctuary by the Nilfgaard after her failed rebellion against King Foltest. While Ambassador Shillard betrayed her trust, the details were never made public and she is seemingly friendly with the Nilfgaard's next likely Emperor in The Witcher 3: Wild Hunt. Access to the White Bridge and whatever troops the La Vallette family possesses gives them a much speedier movement into Temeria from the Pontar Valley.
Nilfgaard wintered down for the time being, only to have King Radovid conquer Kaedwin over the winter. I'm inclined to think there's a variety of factors involved but I'm going to go with Vesmir that Radovid used a combination of the carrot and the stick, defeating political opponents and bribing the rest. Henselt having no heirs was an established part of the game lore and this includes any immediate relations. With the promise of Radovid to restore Northern borders to Pre-War levels, he might have also chosen to play the role of Kingmaker while ruling interim as we see with King Edward Longshanks (Braveheart's depiction aside).
The Fall of Temeria
Nilfgaard proceeds into Temeria only to find Temeria's military fully capable of meeting them head on and the Nilfgaard army engages them in three-days of battle. It's hard to say what happened, exactly, during this battle but I'm inclined to think by the way it's described that it was a situation of "high casaulties, low results." Temeria probably could and did throw everything they had at Nilfgaard in an attempt to break their advance like at Sodden but given the drastic differences between their military strengths, the Nilfgaard would be mildly inconvenienced by their losses while Temeria would be utterly devastated by them.
Real life armies rarely suffer more than ten percent casualties and Sodden was a national horror due to the fact it suffered similar losses. Either way, the Temerian will to resist the Nilfgaard was utterly destroyed and the armies broke up into bandit gangs or deserters or retreated across Velen to join up with The Redanian-Kaedwin Military as their allies. John Natalis was still alive during this time and serving as their Marshal/Charles du Gaulle with day-to-day partisan operations handled by Roche.
Emperor Emhyr personally conducts this campaign with General Voorhis and takes up residence in the palace of King Foltest in Vizima. Mercenary Phillip Strenger proceeded to occupy Crow's Reach and proceeded to assemble an army of deserters and demoralized Temerians underneath him not only to surrender (perhaps a wise choice given the fate of surrendering Temerians) but to engage in full-scale collaboration with the Nilfgaardian forces. From what we see, this mostly engages in looting the region for supplies. Radovid, meanwhile, advances his lines into Temeria and secures Oxenfurt as well as the area around Novigrad.
The Creation of No Man's Land
Novigrad's status becomes something of a thorny subject as a quartet of crime-lords make it so that neither Nilfgaard or Radovid can seize the city's vast treasury as well as merchant fleet. This unusual act at the hands of crime-lords is justified by the presence of Dijkstra, former Redanian spymaster and political enemy of King Radovid the Stern. By promising an end to the city's fleet and treasury, the city is allowed to maintain a brief neutrality. Both sides proceed to start courting the city in hopes of winning it over. Novigrad, notably, at this time was a refuge for powerful witches with numerous ones living in it or the surrounding area and not participating in the war.
Meanwhile, the conflict in Temeria continues both with frequent engagements from King Radovid's forces with Nilfgaard while also Roche inflicting damage on the enemy supply lines. Geralt of Rivia can encounter Temerian resistance fighters stealing medicine from the Nilfgaard and engaging in this sort of asymmetrical warfare during this time. This is rather unusual behavior for the Medieval period but not so much for the pseudo-16th century vibe which the Wild Hunt is mostly projecting, absence of gunpowder aside.
Winning the War, Losing the Peace
We also see resistance is not actually defeated in Temeria as well with The Battle of White Orchard fought relatively recently and a village destroyed, probably as collective punishment despite Velen having been conquered long enough to set up a massive garrison. Stories of war crimes (true or not) like the rape and murder of a Temple of Melitele's sisters distribute themselves amongst the Temerians, which only increase resentment against both Nilfgaardians as well as their collaborators.
Despite their historical antipathy to the Nilfgaard, Skellige chooses to start attacking all shipping to and from their land. This, effectively, isolates the island from the larger conflict and leaves them a nonentity during the conflict. In that respect, this is to Nilfgaard's advantage as Jarl Craite's friendship to Cintra was considered politically significant in the Second Nilfgaard War's councils.
One interesting situation which may or may not have a noticeable effect on the war effort is the invaders run into several encounters with monsters they prove ill-prepared to handle. Griffons, vampires, basilisks, necrophages, and several other creatures Northerners use Witchers to handle result in the deaths of squadrons or larger troop movements. While this is demoralizing and confusing for the Nilfgaardians, I doubt it had much in the way of an actual effect on their military prepardedness.
At this point, the war is effectively stalled.
The Role of Coin
The situation in a standard war between Nilfgaard and the North dramatically favors the former due to the economic might of the Black Ones. Nilfgaard almost successfully conquered the North before the Second Nilfgaard War simply due to its prevalence of manufactured goods. However, the situation proves to be far less stable this time around as Emperor Emhyr's political enemies have made his position untenable. Worse, due to the disruption of trade, the Guilds exert political pressure on Emhyr to end the war and he cannot come to an agreement with them. In short, the Nilfgaard campaign is in dire need of funds or it will collapse on itself.
Conversely, King Radovid is in desperate need of funds for far more prosaic needs. Fighting Nilfgaard is expensive and the only reason the Second War was capable of being fought was due to the presence of vast mercenary armies. If there is to be any victory over Nilfgaard, he is going to need a massive amount of coin to not only purchase mercenaries but also to keep his regular war machine running.
Both men need Novigrad.
The Return of Cirilla
Complicating matters further is the return of Emperor Emhyr's daughter, Ciri, from her transdimensional jaunt across the Spheres. This represents a great personal distraction for the man as the pair did not part on good terms. Likewise, Emperor Emhyr is without issue after seven years of marriage and his dynasty is at stake. Hiring the sorceress Yennefer, Emperor Emhyr also recruits the Witcher Geralt to find their adoptive child. The war takes on a much bigger importance as now Emhyr must defeat his military opponents so that he can defeat his political opponents in order to crown his daughter.
The Fall of Novigrad
King Radovid is acclaimed routinely as a military genius during this time and we get a general sense of this less in his tactics than in his manipulation of politcs. His ability to unite Temerian, Kaedwini, and Redanian interests behind him despite the fact most individuals we meet believing him to be a snake. King Radovid further demonstrates his capabilities by a two pronged approach to securing the allegiance of Novigrad for himself.
The first part of this stratagem is appealing to the Eternal Fire which rules Novigrad. They are natural allies since King Radovid has long been a patron of the previously Novigrad-centric religion. Indeed, it is possible Radovid was a follower of the religion.
The sympathies of the church are exploited by Radovid to launch a large scale witch-hunt in the ensuing months. Triss Merrigold speculates, correctly as we assume, this is not just because of Radovid's antipathy but magic but also as a means of depriving some of the richest citizens in the North of their wealth to fund his campaign and that he will move onto nonhumans next.
This, notably, has no affect on the war effort since the persecution of mages is limited to neutral Novigrad and its surrounding areas. A Conclave-formed via choices by Assassins of Kings backs Radovid against Nilfgaard and will not be targeted until the war is over.
Radovid also breaks the alliance of crime lords by recruiting Whoreson Junior to turn against his fellows through victims as well as other rewards. The breaking of the alliance causes a civil war in the ranks of the four major crime lords and removes their ability to protect the city via their earlier threat. Given Whoreson bankrupts Dijkstra in the process, it's also possible Dijkstra's six tons of gold end up in Radovid's coffers but certainly limit his ability to carry out any operations against Novigrad. It doesn't limit his ability to carry out an operation against Radovid himself, however.
Either way, though, Radovid will enter into Novigrad soon and secure the city for himself. He just may not live to enjoy it.
Reasons of State
Despite semi-successful propaganda efforts to portray him as the North's savior, Radovid's cruelty and untrustworthiness alienates both his soldiers as well as allies. Mages, unlike in Dragon Age's Thedas, had traditionally held important roles in both religious as well as political circles. Their legendary role at the Battle of Sodden made their persecution by the North during a Nilfgaardian invasion seem particularly questionable. It was also obvious to Geralt, if not his mentor Vesemir, that Radovid was unlikely to turn over territories seized during the war.
Dijkstra, despite his troubled fortunes, joined with partisan leader Roche and Temerian intelligence leader Dijkstra in forming a secret peace treaty with Nilfgaard. This treaty would guarantee both their nation's security as well as cede Lyria and Aedirn to the Nilfgaard.
Temeria would become a vassal state while maintaining its own military, leadership, as well as legal code. In effect, it would become an autonomous principality similar to Toussaint. These were exceptionally generous terms of surrender and would merely require an end to fighting as well as assassination of Radovid. Whether John Natalis chose to approve of this treaty or whether Roche and Thaler's influence were enough to force it through is questionable but unanswered by the game.
Radovid Dies (Optional)
Geralt of Rivia, having some small experience with assassination of monarchs, proves a decisive factor in this. Recruiting Philippa Eilhart, they are able to assassinate Radovid in one of three possible resolutions to the event.
In this ending, Dijkstra proceeds to announce he intends to fight Nilfgaard on indefinitely. As Redania's former spymaster and part of the Council of Regents, he has enough authority as well as contacts to continue prosecuting the war from Redania's side, eventually rising to the position of Chancellor.
Unfortunately, Temerian resistance to the Nilfgaard is vital to the continued prosecution of the war effort and Dijkstra's dreams of building a Redanian Empire. Whereas survival for Redania and gains of things like Kaedwin are good, they will mean nothing long-term without Temeria and Nilfgaard's military might has never been at a weaker state due to the economic situation. This is impossible if Temeria surrenders to Nilfgaard as planned.
For Redania to become a rival to Nilfgaard, Thaler and Roche must die.
Radovid Dies but so does Dijkstra (Optional)
In one case, Dijkstra's choice to assassinate Roche and Thaler in front of their occasional ally and possible friend, Geralt of Rivia, proves ill-advised. Without Dijkstra to either inform the peace or lead Redania's forces, the country is left leadership during a crucial time during the war as well as bereft of their Temerian allies.
Radovid Dies but so does Roche and Thaler (Optional)
In another case, Geralt of Rivia proves disgusted by Roche and Thaler keeping him out of the loop regarding the secret treaty of Nilfgaard. Also, perhaps feeling some affection for Dijkstra for his role in helping the mages of Novigrad, he leaves Roche and Thaler to divest themselves of their problem on their own.
They prove unable to do so.
In this case, Dijkstra maintains Temerian dogged resistance to the Nilfgaard as well as takes over the Redanian military's efforts.
Radovid Lives (Optional)
In another case, Geralt decides that he is not an assassin, even of tyrants and focuses instead on saving his daughter. In this case, Radovid finds himself in possession of not only Novigrad's fortunes but Temeria is unable to secure a separate peace, forcing them to continue fighting in the service of an individual who wishes to conquer them.
The Disaster at Skellige
During the final stretch of the war, Emperor Emhyr makes a curious to invade Skellige. This is an action which opens up a new front in the war in which Nilfgaard is already having difficulty defeating Redania. This isn't something Nilfgaard doesn't have the resources to do as Skellige is a relatively primitive island chain and sparsely populated. Their status as a warrior culture and vast number of sailing ships would not be able to prevent their conquest in the shape of a sustained military effort by Nilfgaard, especially with the historical clan divisions of Skellige.
Unfortunately, for Nilfgaard, that's not what happens.
After these events, the final weeks of the war begin. Or, at least, the Temerian front.
Nilfgaard Wins (Optional)
Nevertheless, if King Radovid and Dijkstra are dead, then the peace-treaty with Temeria is signed and Nilfgaard's former enemies become their allies. This allows a complete withdrawal of the Nilfgaardian soldiers used to garrison the nation and their deployment for a push into Redanian and Kaedwini territory. Without Temeria's partisan efforts and need to occupy the region with thousands of troops, it is seemingly only a matter of time before Redania and Kaedwin fall.
Redania Wins (Optional)
With the disaster at Skellige and the acquisition of Novigrad's considerable wealth as well as trade fleet, King Radovid or Dijkstra is able to push their forces to Vizima which results in a necessary Nilfgaardian withdrawal from that city. By that time, Emhyr's political fortunes have reversed to the point that he is suffering non-stop assassination attempts. One of these assassination attempts will eventually succeed and Nilfgaard will have its own difficulties to deal with rather than Emperor Emhyr's failed military adventures.
Thus is the history of the Third Nilfgaard War.