Alright, simply because I feel it's necessary, I'm going to attempt to banish most arguments before I share my personal opinion. Most arguments are based on:
Aldmeri Dominion's involvement
imperial reinforcements/stormcloak military strength
Local support
I'm discounting both weather and supplies as both have been satisfyingly disproved.
If you speak with Tullius he says something along the lines of him not getting many reinforcements due to the legion needing their troops in Cyrodil. Also the stormcloaks military strength is significant enough to be a threat. True, the empire has the numbers advantage but not by a whole lot when speaking in terms of an army.
Local support in most cities is leaned towards whichever faction is in control at the time with the exception of Whiterun which is effectively split and Markarth which actually shows a surprising preference towards the stormcloaks.
The Aldmeri Dominion's involvement is something of a wild card. They want to see that the war continues, however no one can truly be sure of how they would respond to certain scenarios.
This, the AD and the Empire can't risk over extending their troops for fear of being counter attacked by the other when they're weakest. And Skyrim isn't a provence like Cyrodiil, it doesn't offer a ton in terms of strategic military advantage. The risk v reward isn't there...
It'd be like the US sending all of our troops to Alaska and leaving the heart of America vulnerable.
I must say that while that WOULD be solid reasoning, Skyrim is actually VERY important to the empire. If the empire lost Skyrim, They would only have Daggerfall and Cyrodil, separated by two independent nations. Being split like this would eventually result in Daggerfall becoming independent and leaving Cyrodil on it's own, benefiting the Aldmeri Dominion greatly.
And finally, the argument that Ulfric would have had his head chopped off in Helgen:
Honestly, this part of the game is all messed up anyways. Darkwater crossing close to the border: wrong; Plus what would he even be doing out there? Has anyone seen him leave the palace before the battle for Solitude? This was put in the game by Bethesda to expose the player to the war early on and otherwise makes no sense realistically.
All that being said: The war wouldn't end. The Imperials would likely take control of Dawnstar and winterhold and after a very bloody battle and feud in Whiterun their advantages would mean the Imperials take the city. Continuing their march they would take Riften without a struggle, Maven would stage her own Coup and hand the city to them, taking advantage of the war rather than allowing it to harm her business. The Imperials would then march on Windhelm and stop, The remaining stormcloak army would have superior defensive advantages and cause enough damage to the Imperial army that by the time they reached the city they would only be able to lay siege to the city, not take it.
I know that this goes against my previous argument, but this is where the Dominion gets involved. They would ensure that Windhelm was properly supplied in order to hold against the siege and the Imperial army would eventually be weakened and forced to retreat. The Stormcloaks would then be able to easily retake Dawnstar, Winterhold and take Morthal as they are not very easy to defend and would likely take Markarth simply because they would have local support. I'm talking about the people, not the frosworn. The people fear the Forsworn and would likely welcome their one time "saviour" plus the silver blood's support. With the rest of Skyrim cut off from Solitude they could easily take Falkreath as it's very hard to defend and again Riften would be handed over, so long as Maven stayed Jarl which she likely would. Whiterun would be surrounded and would simply surrender. Jarl Balgruf, while he despises Ulfric and does not believe his cause, has no true loyalty to the empire and cares more for his people than for the war. Solitude would be besieged and would be able to hold out easily due to effectively being able to resupply by sea. The end is either that the Thalmor throw themselves in and this cycle repeats almost endlessly, or the Thalmor see the advantage of cutting off Cyrodil from Daggerfall and that supplies would be wasted on holding Solitude.
That took alot to say but realistically, without a miracle or chance/fate's role, this would be the result. I hate that I've come to this conclusion because I support the Empire, but that is just the logical eventuality.