Same thing in America. I've never ever heard of anybody ordering TEA and someone getting confused that it's not supposed to be hot. I waitressed years ago and when someone asked for tea I never said would you like that tea hot or cold? When we want cold tea we say iced-tea. We always say iced-tea on this side on the pond...always! The only thing we may ask about the ice tea is if it's sweetened or not. Can I get an Amen from my fellow Americans on this very very important issue.
You may get one from me. I order tea quite a lot, actually (I loathe coffee, and I like soft drinks only every now and then), and if I want iced tea, I say "iced tea." If I want hot tea, I'll just say "tea" or perhaps "a cup of tea." Sometimes I then get asked if I want it hot or iced, but not usually, and thus far, nobody's assumed that my request for "tea" meant iced tea. Could happen, but it hasn't happened so far.