1. Tiber Septim was a Nord, and the only real reason he conquered anything was because he used the dragon shouts (and the Numidium but that's gone).
2. There would not be a race war, it would be between the different countries (An Argonian, born and raised in High Rock, will not walk all the way across a continent to fight with other Argonians).
3. Skyrrim has the only known person to use dragon shouts, thus Skyrim would win that war making Nords the official winner of the war.