My two most recent trips were SIN->HKG and return. I didn't wear my coat in the airport
These days, I usually try to travel with nothing heavier than a suit jacket and a wool sweater, if I'm going to the more temperate regions (like some of the places you people list in your profile locations). If I were going to, let's say, Chicago or Moscow in the winter, I'd probably wear a heavy coat, but I wouldn't wear it in the airport in SIN.
I used to have a nylon jacket, with zip-up pockets. Then I'd put everything in the jacket pockets, and at security checkpoints, all I'd have to do is take off the jacket. (Except in the US, where shoes would have to come off, and you get the anal probe or whatever it is they're doing these days.) In most of Asia, though, the security screening is sufficiently civilised that I would just wear my coat if the weather were cold, and take it off at the checkpoint without feeling like I were gumming up the works.