My only experience shooting in temperatures as low as that was more than 50 years ago when I was attending college in northern New Hampshire. I had a Honeywell (Asahi) Pentax H1a SLR, and mostly used it with the manufacturer's "kit" 55mm lens. No issues with battery life in those days: the camera was entirely mechanical. I do distinctly recall one winter morning when a classmate banged on the door of my dorm room at the crack of dawn and announced that we needed to shoot some pictures of the campus in new-fallen snow. We were outside for a couple of hours and I don't think I felt particularly cold, but late in the session I pulled the camera away from my face and took a big chunk of skin from my forehead with it. I decided there and then that cold-weather photography would never be my forte.