If we take it as gospel that "if you're cold you can't trust your mind at all because you may be hypothermic and not thinking clearly"...
Who said anyone came down from Mt Sinai with the commandment "Thou shalt not sleep if you're cold..."?
Of course, if you can still think clearly, then you're not that far gone, no matter how cold you feel. Same thing if you're still shivering. But once you stop shivering or once you start noticing that you can't think clearly and have trouble concentrating, you've obviously entered a more serious stage.
I saw this TV show once where alpine mountain climbers swallowed temperature sensors. The data showed that the climbers core temperature stayed up as long as they kept moving, slow as that pace might be at extreme altitude. If they stopped, some climbers were able to maintain a tolerable core temp, but in others, their core temps immediately started heading down to dangerous levels until they started moving again.
So, when you're that close to the borderline, the ability to differentiate whether you can stop and rest or whether you are in danger of severe hypothermia is critical. But if you're already near that point of hypothermia, that's kind of like asking a person who's been drinking heavily to assess whether they are safe to drive. (A clear headed buddy is helpful in both the hypothermia and DUI scenarios!)
Actually, this physiologic difference observed in the TV show probably partly explains why some people in dire straits can fall asleep and survive, while others succumb to the elements if they drift off to sleep. People come to differeing conclusions based on such survival stories, but miss the possibility that the people were quite different in some crticial way.
Look, you're also going to be fighting other reasons for wanting to sleep--physical and mental fatigue, dehydration, malnutrition, lack of sleep, shock, injuries and/or blood loss, maybe side effects of your normal prescriptions or OTC meds, maybe side effects of a Vicodine you took for an injury--so it's not an easy thing to sort out whether you're sleepy from late stage hypothermia or other reasons and whether it's OK to sleep.