I'm sure it plays a role, but I don't think it is determined only by where they are from or how exposed they have been to playing in the cold.
There are tons of guys from warm weather areas that have shown they can play at a high level in the cold. Some can't.
This has to be one of the last things I would consider when evaluating a prospect, though. There are so many things that are so much more important than this. Unless the player is making comments about it, then you might want to stay away because it shows they are conceited and weak. The message you want to hear is, "I'll play anywhere. Cold, hot, rain, snow, whatever." If they are whining about the cold as draft prospects, that's a character concern.