Great question — answering as the UphillTech team:
I am not a doctor, so I can only repeat what I think I understood from lectures by those that do have medical training. I'm pretty sure I remember Dr Murray Hamlett (I highly recommend attending one of his lectures, if he's still doing them. He is not only a leader and pioneer in cold weather medicine, but also a very good and engaging speaker.) saying to keep the patient awake. I do not remember exactly the reasons he might have given, but keeping the internal metabolic activity as high as possible sounds like an advantage to me. Basically, we burn fewer calories, and therefore produce less heat, when asleep. It is also more difficult to assess a patient's state when they aren't fully...
Full answer by Olin Lathrop: https://outdoors.stackexchange.com/a/3805 (CC BY-SA 4.0).
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