i would assume that the "don't fall asleep" advice comes from the old days when hypothermia was not well understood.survivors would tell of others in the group who fell asleep and died not understanding that sleep was part of the hypothermia process.
my favorite "don't sleep" story is out of a old--1950's--TV program where the hero would not let a bottle of whisky be drunk up because when it froze he would know it was 40 below.i don't recall what was going to do then!!!???