I think the importance of who won could be marginalized by the passing of time anyway. You could have 2 scenarios yield similar results with a 2nd Great War opening up:
Scenario 1: Empire won the civil war but now since a new war is starting, the terms of White-Gold no longer apply thus soothing much of the divide in Skyrim's Nords over the Talos worship-thing. Skyrim then is likely a bit more autonomous while still aiding in the new war with a common enemy.
Scenario 2: Stormcloaks won, giving them autonomy but likely still close ties with the empire. With a new war starting, their shared enemy gives them reason to fight alongside the Empire. Like in scenario 1, most of the underlying divisions are no longer present or all that applicable either because of the civil war result or because war is back on with the Dominion.
Also given enough of a window of time between the end of SR and the potential start of new hostilities, it could be such that most if not all the powers-that-be in SR in the 4E 200's are no longer alive and it's a completely new generation of leaders with different mindsets, strengths and problems altogether.
If I had to put money on it though, I think the official story would be something like the middle-ground scenario possible in SR where there is a negotiated truce between the sides with each side having more influence/controls in certain holds, that is to say that neither achieved total victory.
Ultimately when it comes to war with the Dominion, that will override existing animosities to a good extent. For instance, do you think Hammerfell would stay out of the war just because of anger over how they were officially shafted by the Empire w/ W-G?