My layman's understanding of hypothermia is that, barring something like immersion in ice water, it's not so much that your core temperature simply gets too cold, it's that your body runs out of fuel (blood sugar) to burn.

Or: You don't stop shivering when you go from mild to severe hypothermia, rather you go from mild to severe hypothermia because you've lost the ability to shiver.

I can't see how it matters if you're awake of asleep, unless there is some action you might take to improve your situation while you're awake.

I suppose one rule of thumb could be that find yourself shivering, you might want to get up and perform some useful work instead.