An interesting topic. How reliably do hypothermic people recognize that they are hypothermic? Since hypothermia starts affecting your cognitive abilities, I think it would be quite easy for a severely hypothermic person to "forget" the fact that they're hypothermic.

I once saw a show on Discovery Channel that described the final stage of hypothermia, which includes extreme sleepiness, before the person drifts off and dies. Maybe that's the scenario that people are trying to put off?

I have read or watched TV about quite a few cases of survival from all kinds of dangers like trauma, disease, starvation, etc., where people instinctually told themselves to stay awake and concentrate even though their body was telling them to just give up and go to sleep. Arguably, these survivors should have succumbed, but somehow they survived. Was it willpower? Could be.