So I played through the Stormcloak campaign as a Nord, and as expected there was a lot of nord pride stuff going on throughout the whole plot. What I was wondering, is there any difference between playing through this plot as a nord, and as another race such at high elf, dark elf, argonian, khajiit, etc? I know that Ulfriic is pretty anti-anythingnotaNord, so I would assume there would be some different dialogue or something.

No, people are a bit more insulting if your Mer or Beast but otherwise its the same game. Altmer with a hooded thalmor robe can sneak through half the embassy. Ulfric himself doesn't seem to care so long as your willing to fight the empire.

Your story arc can be whatever you make it. Using the miscellaneous quests and favours, you could play a Dunmer who drives the Stormcloaks out of Windhelm and makes a lot of Dunmer friends along the way.

There's very few minor difference, mostly dialogue. Nothing physical - for example a khajiit can freely waltz into whiterun even though the cities won't let any OTHER khajiit through the gate

just the way people treat you thats it