Many novelists and some over sources have described the "fall asleep and never wake up" phenomenon.
On the other hand many good sources describe this as a myth and a misunderstanding.
As far as I understand it, you may be exhausted, on the brink of hypothermia, in which case let yourself go might proove fatal.
On the other hand, if you go to sleep from an healthy position, if ,let say, your sleeping arrangement is defective and you're quickly loosing heat, cold will wake you up at some point. Doesn't mean you risk nothing, but you shouldn't die quietly without realizing what's going on (again we're not counting here situations like extreme exhaustion, drunkness...).
Basically: yeah. The fall-asleep-to-never-wake only happens when you're already in severe hypothermia. If you at no point feel really cold, then that is not going to happen. (Although you can still get a nice big heart attack in the cold, especially after much skiing or walking and camp building during the day, if you're physically in a poor condition.) But one needs to keep an eye out on how cold it feels and how the body is responding to it.
When it's actually really cold, or rather more accurately too cold for you and your gear, it goes pretty much like this:
1) you start to feel cold
2) annoyingly cold (you should be doing something to get warm by now, or it's going to be bad)
3) painfully cold (last chance...)
4) until suddenly it doesn't feel half bad anymore (congratulations, it's hypothermia!)
5) well, you do feel a bit tired (time to call someone to save you now)
6) really tired, actually
7) I'll just sit down here for a moment, you guys go on ahead
8) whoops, you just died
On the other hand, it
doesn't go like this:
1) you feel pretty nice - okay, so it's cold, but you've got a lot of clothes to keep you warm and nice warm food and drink, mostly it's just that the cold stings your face a bit - should've brought a mask of some kind. Oh well, that's what the fire is for.
2) some hours of working and setting up camp later it's about 11 PM and you feel a bit tired, way past your usual bedtime. Still feeling pretty warm, though, time to go to sleep.
3) you crawl in your warm sleeping bag next to that nice campfire
4) you fall asleep, feeling pretty comfortable, especially now that the wind doesn't sting your face when you're almost entirely inside the sleeping bag
5) you never wake up, because you mysteriously freeze to death
What would happen is this:
1) you feel pretty nice in the sleeping bag, and didn't feel very cold at any point during the day, thanks to heavy clothing and a nice fire
2) you fall asleep
3) maybe the fire dies out, maybe the night is much colder than the day - that's how these things go...
4) you're starting to feel cold in your sleep
5) really cold
6) damn, I can't sleep in this cold
7) you wake up, feeling damned chilly and ready to kill whomever was supposed to keep the fire going through the night and failed to do so
8) cursing, you run and jump around and make some tea and build a real blazing inferno of a fire to warm up again
