Imperials didn't storm into anywhere, the Nords joined the Empire before Tiber Septim even became Emperor, that was the Second Era, it is currently the Fourth Era during the events of Skyrim. The Nords and Imperials conquered Tamriel together, the Nords have a long history of invading other races, such as The First Empire of the Nords, or during the Imperial Simulacrum where Skyrim invaded High Rock and Hammerfell taking over many miles of land. The Nords themselves have been known to subdue native races, such as the Snow elves and even the Reachmen (Of whom the Nords forbid the natives of the reach from worshiping their own Gods.)
Imperial authority brings peace and stability, the last time Imperial authority was low all the provinces were at war with each other, the Imperials are hardly evil tyrants. Windhelm is Skyrim away from Imperial authority, racial segregation and a city falling apart. Growing food in Skyrim is actually rather hard due to the climate, very few farms do well (exception being Rorikstead) The Nords used to raid other provinces for things, they can't do that in the more modern times of Tamriel as more lands are united. They depend on the Empire for many things, you can't feed the population with the grand speeches Ulfric makes.
"Because the Dominion is a sleeping beast that Skyrim cannot slay alone. Because many Nords are part of the Imperial army even now. Because the food and resources we get from the Empire are important to our people. Because even if we can't openly worship him, Talos the god was once Tiber Septim the man, and this is his Empire."
The Imperial Legion is made up of many races, the Imperial Soldiers you see in Skyrim aren't just the race Imperial but many are in fact Nords. You also have a Dark Elf Legate and a High Elf Legate, many Orcs join the Legion as smiths and heavy front line infantry.
The Imperial Legion has been in Skyrim for hundreds close to a thousand years, they're hardly Invading. The Civil war isn't Imperial vs Nord but infact Imperial, Nord, Dark Elf, Breton, High Elf, Orc, Redguard, Wood elf (The Empire has many races that are citizens) vs Stormcloak