You should pee.

Your body creates it's own heat when healthy and fed and you will easily compensate for loss of 100-200mg of body mass in all but the most extreme conditions.

By the time you are so cold or in such a place as to be at risk of losing a meaningful amount of core body heat from urinating  , I suspect your body functions will have shut down and you wouldn't have needed to pee in the first place.

For what it is worth alpinists, mountaineers, everest climbers will pee and poo all up and down the mountain.

You should pee.

Your body creates its own heat when healthy and fed and you will easily compensate for loss of 100-200g of body mass in all but the most extreme conditions.

By the time you are so cold or in such a place as to be at risk of losing a meaningful amount of core body heat from urinating, I suspect your body functions will have shut down and you wouldn't have needed to pee in the first place.

For what it is worth: alpinists, mountaineers, Everest climbers will pee and poo all up and down the mountain.