While it does seem to make sense logically, this is Dnd and sometimes logic doesn't play into things. Cold spells are really really cold, much colder than a night in antartica, or at least so much of that cold shoved into 6 seconds that a thick coat and various layers of wool fabric just don't cut it. Also, to do so would give a very cheap way to help save against cold spells which wouldn't be fair to those icy hearts of wizards and sorcerers out there.
Tellerve