I've woken up shivering ... probably in early stages of hypothermia. Happens if you forget your sleeping bag, and you are above the freezing level. Hahaha! Doesn't happen often though - you LEARN not to do that :-)

The stories where people are telling each other not to go to sleep usually are expeditions to high mountains and polar regions. In those conditions, the adventurers are already in a pretty serious situation - they already have serious hypothermia, they probably have some frostbite, they don't have any food (or heating supplies) left, and they may be low on oxygen. So these are not just people who are feeling cold - they have fading life signs. In that circumstance, I would think that you probably could fade out mentally and just be gone.

Pete2