A united Nord force would have very little difficulty with the Aldmeri. The Nords spent years fighting with the Dunmer. The Nords are the only race to ever take land by force from the Dunmer (When going toe to toe, the crisis in Morrowind now excluded). No enemy has ever fought the Dunmer successfully and won (Look at the Imperials), The Nords unified could lay waste to any force the Aldmeri could and would field (The Dominion lost all it's armies it sent to Cyrodiil it would be an absolute disaster if they set foot in Skyrim).
Khajiit Overlord Rainer hit the nail on the head.
While a united Nord army would be strong it would still be no match for the entire Dominion. The Dominion knocked the most powerful army on Tamriel around and conquered half of her provinces. Facing a single province of, as Overlord said, divided and even more battle worn warriors would hardly prove impossible.
You must also consider battle tactics.
The Dominion is largely Altmer. One can assume that a core aspect of their army are their Battlemages. Not just your regular run of the mill mages but battle trained, battle harden mages. The Nords are, for the most part warriors who shun the magical arts. The very landscape of Skyrim actually FAVORS the Dominion. Nords have to get close to do damage, the Aldmeri Battlemages would, and could, rain death and destruction upon the Nords well before they ever got into range. The hilly and mountainous landscape even plays in favor of a ranged magic army. The most favorable landscape for the Nords is around Whiterun, in the plains.
The Nords will be facing an entire army of trained and disciplined magic users. Even their infantry wields magic to some degree. While the Aldmeri would be hard pressed to fight the Nords in physical combat they would absolutely decimate them at range. They would know this as well and they would use it to their advantage. 50% Resistance to Frost spells wouldn't help either as the entire army would be smart enough to use only fire or lighting on the Nords.
The Nords were crushed by Elves before, in Ysgramors time. Ysgramors only saving grace was that he was able to flee back to Atmora and collect a new and massive army to return with. The Nords of Tamriel have no such haven. Were they to be crushed by the Dominion they would be hunted to extinction as the Aldmeri would know the Nords are unlikely to ever lay down their arms. Not to mention they're vengeful and would likely seek retribution to how the Nords treated the Falmer.