I just created this account to post an idea that I have not read here yet.
First, I like the previous comments a lot that suggest that the white-haired witcher (/Geralt) and Nimue in the epilogue could represent Sapkowski and the readers. It certainly seems that there are many parallels; Nimue's questions are often the ones asked by fans, and the responses provided are the ones Sapkowski tends to give (or intentionally does not want to give). But beyond the message Sapkowski wants to deliver to the readership as Sapkowski, I am sure that this epiloque also has a meaning relevant to the story.
Second, the idea that the witcher here could be an illusion-Geralt created by the daughter of the vixen. It seems a very reasonable explanation that makes a lot of sense.
I want to introduce another idea that I found attractive if not assuming an illusion (which is of course always a kind of easy explanation). This is speculative, of course, but I try to support it with the limited material we got:
The white-haired man never confirms his identity, he even talks about Geralt as someone he knew well and had a friendly relationship with (e.g., him saying Geralt would probably be happy if he knew people would still remember him and even the name of his horse). It is fair enough to take for granted that the white-haired man is a witcher (two swords, fighting a monster, collecting a sample, knowing Geralt well and seemingly personally from long ago). White hair itself is not something very unnatural or rare, it is just that we do not know other witchers than Geralt with white hair because witchers age slower and they usually die sooner or later in combat before they grow old (not in terms of years, but biologically). This was once stated by one of the witchers in Kaer Morhen in one of the canon books, so we can consider this as true. In addition, it is canon that there are only a few witchers left and "reproduction" is to be expected very unlikely.
At the time of the book series, among the few witchers, Vesemir is certainly among the oldest if not the oldest. If he did not die for another 105 years after what that white-haired man referred to as Geralt's death in the epilogue, then Vesemir could probably have naturally white hair by now. Even if we want to believe that naturally grown white hair was not as bright white as Geralt's famous hair, we must consider that Nimue in the epilogue has never seen the real Geralt. She just knows the stories and now sees a white-haired man with two swords killing a monster (and it was dark..). So, it could easily be an even older Vesemir with naturally white hair. Also keep in mind that Nimue was obsessed with the stories about Geralt, Ciri, and Yennefer. So, it is very likely she would believe to see Geralt whenever she meets any man with white or grey hair, two swords, with a horse..
The way how this white-haired man talked to Nimue reminded me more of how conversations between Vesemir and the other witchers were betrayed in the other books (i.e., more like a warm-hearted father figure, lecturing at times, but not as harsh or blunt as Geralt or the other younger witchers sometimes have been with Ciri).
Also, the actions of a (potential) Vesemir make a lot of sense to me: He may know about Geralt's story in the Season of Storms and may want to finish Geralt's uncompleted tasks. Also, Ciri may have told him about everything that happened in the canon books, including Nimue and how she helped her in a different time line. So, this means that Vesemir has a special interest to guide her on her path to fulfill her destiny (which is to help his own dear friends-of-the-past in the future) when he realized who she was. And this is exactly what the white-haired man did and told Nimue (i.e., he helps her literally to get out of that forest, he guides her onto her future path, and he tells her that she has a specific path to go that is different than his). He is reluctant, rightfully so, to tell her the plain truth about Geralt's story and about his identity because he sees that her believe in the stories is the prime motivation to pursue her path and to become what is required to fulfill the important role she will have in the future.
The Vesemir theory is supported by intro before chapter 1 and this is also the reason why I got this idea in the first place: There is this small intro before chapter 1 where a quote was cited about the dark in the world, that there will always be evil hiding in the dark. This was quoted from Vesemir in fact, and it is extremely similar to the words of the white-haired man to Nimue. Now, one could argue the same for the quote of the vixen (i.e., "illusion.. all is illusion"). However, I first find it way more suspicious that the comparably long quote from Vesemir is almost identical than the very short one of the vixen. Second, Vesemir has a good reason to say that to Nimue, too, because he does not want to take that illusion from her and, thus, he fuels her curiosity that eventually will make her fulfill her destiny. Third, we can even imagine that Vesemir knows about the encounter between Geralt and the vixen as it was a rather extraordinary story in Geralt's life (otherwise why would Sapkowski tell us this one) and they met a second time in the book's last chapter before the epilogue (maybe even more times later). Anyway, I found it reasonable that Vesemir knows about the story and perhaps even this quote. Maybe he likes it and that just made him use it, but more importantly, as pointed out, he had good reason to say that anyways.
Critique: Some may ask why Vesemir, if it was him, asked Nimue for the year, and some may think that this question is proof that the white-haired must be a time-traveler or such kind. I do not think so, and I could imagine that Vesemir was not asking this because of having no idea whether the present is before or after Geralt's death but how many years exactly already passed. This would make sense because the conversation continues with him expressing his surprise that people still remember him nowadays. So, my explanation is that Vesemir at this time has lived a really long life and perhaps he was traveling a lot alone during the last 100 years when Geralt and perhaps also the other wolf witchers died (one died during one of the battles in book canon, so there are only how many remaining? 2?). So, it is easy to imagine that he has a different sense of time, years, and memory compared with regular humans. So, assume he is Vesemir, traveling alone, honoring Geralt's life by completing some of his tasks, living the witcher life as the last one of his school perhaps, he is probably not too much interested in politics and what is going on in the regular human's world except for the good and the bad and to protect humans in general (no matter the time) and he may have disconnected a bit with what is going on. So, a rather young girl is now talking to him about Geralt, Vesemir may be surprised in the first moment because in regular human terms (which is not Vesemir's perspective) she is too young to have experienced that or heard as a story by her parents or even grandparents. So that means the stories have become more of the caliber of legends. And that is something not so obvious for him as for us when a young looking one talks about it 100 years later because he has a different sense of time, so he needs to reevaluate. So, in my opinion, this question could be less of an indication of someone time traveling and more like "wait a moment, what year is it exactly? hm.. that means it's already 105 years since then, that means a crazy long time for these regular humans".
What do you think and do you have other critiques on this theory?