As understand it it isn't a question of sleep or not to sleep. If you are hypothermic you need to be taking action to warm up or better protect yourself. Sleep in this case represents failing to act and allowing the process of hypothermia to continue to advance. The likely outcome would be grim.

Yes, hypothermia, especially coupled with dehydration (I'm always surprised how much warmer I feel if I'm well watered), hunger and fatigue, can cause you to feel like someone 'pulled the plug' and to feel strongly compelled to sleep. But it isn't the sleep that gets you. It is sleeping instead of actively correcting the situation.

Also, in my limited cold weather experience and understanding, if you went to sleep warm you are going to wake up long before hypothermia sets in. Of course this is greatly helped along if you are also well fed and watered, and not gravely fatigued.

I have talked to people who claim that in extreme cold, even outside hypothermia, that you better not sleep. As if the combination of sleep and cold was somehow toxic. Like the Sandman and Jack Frost get together and set about slitting throats.

Staying awake when not in actual danger of hypothermia sounds to me like a fine way to get into trouble by way of fatigue and sleep deprived confusion. Lots of survival situations went bad when people got so fatigued that they couldn't think straight and made some dead simple rookie mistake, or simply walked around in circles. Sleep is as vital to survival as food and water.