I'm extremely late to this party but I wanted to document a little evidence form within the game that hasn't been mentioned elsewhere in the answers here; the Stormcloak Missive in Fort Neugrad (transcript below).
Though we drove the Emperor's dogs from Fort Neugrad, they still nip at our heels. The chaos in Helgen is bad enough, but now I have word of a new Imperial force assembling in the south, ready to advance on our position as Pale Pass is clear. Send reinforcements, or all our gains will be for naught.
This only appears under certain conditions which I believe are that the Dragonborn handed Falkreath to the Stormcloaks during Season Unending and then joined the Imperial Legion to retake Falkreath.
This missive indicates that there is a "new Imperial force assembling in the south" which is preparing to move in to attack the rebels in Skyrim. The desperate wording could indicate either; the soldier is worried about losing their foothold in Falkreath or, he is worried about losing the war. The fact that the Emperor has assembled a Cyrodiilic Legion force with the purpose of sending them to quell the rebellion in Skyrim demonstrates that the Emperor does indeed take the civil war seriously, despite assertions to the contrary from some NPC's. As such, since the Legion isn't being used to fight battles within Cyrodiil at the moment it would be quite reasonable for the Emperor to send a large force to assist the army in Skyrim.
How is this a relevant factor given that the Stormcloaks are already in a stalemate with the Empire? The Skyrim Legion is composed primarily of local Nord recruits - individuals not much better (if at all) than any Stormcloak soldier, except with arguably better equipment. Likewise, some Legion veterans since joined the rebellion, leaving both sides with a number of experienced soldiers and novice recruits. The tipping point is the force from Cyrodiil being a full Imperial Legion of well-trained soldiers, not local Nordic farmers.
While we can but speculate the outcome of a Stormcloak vs Cyrodiilic Empire war it would be fair to assume that the Cryodiilic Legion would be more effective than it's Skyrim counterpart and able to overcome a rebel force, leading Skyrim to an Imperial victory.
Thus, whether the war is left unresolved or as a Stormcloak victory the southern Legion force would still (re)take Skyrim for the Empire.
Other answers have mentioned the Dragonborn becoming some kind of leader or overshadowing the events of the Civil War - this would be very out of character for Bethesda lore. Historically, every TES hero has played a role which is equivalent to the respective game's main quest line (and subsequent DLC quest lines). No more, no less. To say the Dragonborn will become a heroic leader of an entire army is very speculative since, based on all previous heroes the Dragonborn's story ends with the defeat of Miraak on Solstheim.