Another thing I'd like to add. It SEEMS to make sense that if you're cold, the body might divert energy from the immune response in order to keep the core temperature stable. However, I can't find ANY evidence.
In fact, there seems to be a fair bit of research, yet no link between exposure to cold & immune response (except possibly in the case of actual hypothermia).
If anyone can find any evidence to the contrary, please share!
However, it's looking like that one might be a myth too. A myth with a believable mechanism, but a myth nonetheless.