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.
Amen my American brothers and sisters! If I want iced tea, I say iced tea. If I want hot tea, I say hot tea. There's little ambiguity right there.
Plus the setting you're in often dictates things. If I walk into a diner for lunch on a hot day and order up a burger and fries and a big glass of tea, it's pretty much implied that I want iced. Same thing if I'm at a restaurant and the waiter is asking me what I'd like to drink with dessert. It's implied its hot.
As for Picard, maybe he just wasn't a preset guy. I barely have any numbers programming into my cell phone and none at home. I don't have an address book in outlook. I don't have any presets on my XM radio. I'm just not a preset guy.
Plus it was one of his trademarks.