In reply to Stani49:
Something small enough to keep warm in an accessible upper pocket (with a neck cord so you don't drop it), but not so small you can't push the buttons with gloves on. e.g. I could not operate a Sony RX100 with gloves on. My Canon S100 is just OK.
Preferably something you can shoot one handed with. i.e. no removable lens cap.
Take at least two or three spare batteries. Easier than recharging.
It's using the cam in the cold that will kill the batteries. Altitude is irrelevant.
I've never thought much of the image quality of the Panasonic Tough cameras, but maybe the very latest ones are better.