That's a Greek Corinthian-style helmet, not something the Roman soldiers wore, and the Imperials are modeled after the Romans, not the Greeks.
As far as the amount of clothing goes, it's a fair point, but vast stretches of Skyrim are not that cold, and not portrayed as such - thankfully. When I first heard about the game I was excited, but simultaneously afraid that the whole place would look like a monotonous, snowy hell. Thankfull there is a lot of diversity of climate.
Yeah, I was wondering why they had that style of helmet. One thing I did notice about it though was that that kind of helmet is completely closed. All parts of the helmet join together over the face. In real life they are more open. A plumed imperial captain helmet would look more roman. Perhaps the alternate helmet is a sort of reference to the plumed greek style helmets in oblivion.