I’m not sure how cold you’re talking about, but having done -30 on a windy lake at 2 in the morning, I’ll give a shot at this, and I think what I’m gonna say would apply to colder temperatures too.
Dress *very* warmly. I mean, excessively warmly. Thermals, sweater, and windbreaking winter coat, wool socks, snow pants, or whatever you do in that regard. Pile it all on – while shooting, what you mainly need is warmth, not agility. Strategically speaking, you want something warm and fuzzy near you, to keep warm air around you, and something air-resistant on the outside, to keep the wind and cold air out. If I dress warmly enough, my hands get cold less fast, despite severe raynaud’s in my hands. Then wear some kind of leather or rubber glove, that is thin, and yet cuts airflow completely. I find I can operate most of the controls without even taking off the glove. You also want a glove that doesn’t have liner that keeps coming out, so you can quickly at easily get them on and off. Keep your gloves on as much as you can. Use a tripod. Sounds irrelevant, but it means you can set your camera down at any time and slap yourself, or dance a jig or whatever to get the blood flowing. Set your camera on a tripod, and can use one finger at a time to get to the different buttons.
In regards to technique, shoot in some mode of automatic. It means you don’t have to do as many adjustments. If you learn the automatic modes, you can set up the important parameters yourself and have the camera’s computer do the rest. I use aperture priority a lot for landscapes, or manual with auto-iso for animals.
The other thing I have never practised, but probably should, is in regard to warming up your gear. When you bring a camera indoors, after being in say, below 10 below freezing. (That’s what, 15 Farenheit? sorry, I’m used to Centigrade temperatures) They say to take the memory card out while you’re still outside, then put the camera and lenses in a camera bag and leave it closed for a couple hours indoors before taking them out again. This allows the gear to heat up slowly and keeps humidity from condensing on the electronics inside the camera. I never took the trouble to do this, and never had a problem, but that’s what they say to do.