There's been a lot of discussion about battery life in cold weather and the simple solution is to keep the battery in a warm pocket and insert it when you take a shot.
Another very important cold weather shooting issue I've discovered is that you should hold your breath while changing lenses. I've had whole series of shots ruined by condensation on the sensor. The condensation evaporates rather slowly and stays longest in the corners. You don't have to be breathing right into the camera chamber either. Breath fog can spread out quite a ways in very cold conditions. Better safe than sorry; it's not very difficult to hold your breath long enough for a lens swap.
We had a long thread recently about gloves. Here's my real life findings after 3 weeks of non stop very cold shooting. A thin pair of cloth stretch gloves lets you handle your camera controls and is adequate down to about 40 degrees. For lower than that I use a pair of mittens with flaps to expose fingers and/or thumbs and the cloth gloves under the mittens. That's good to about freezing temperature. When you get down to around 20 degrees or lower, even the double glove system is not very effective. Your thin glove clad fingers start to sting and get numb almost immediately when you pull the mitten flaps back to take pictures. For that situation I've bought a couple of cigarette lighter fluid powered hand warmers to keep inside the mittens next to my fingers and palm. The throw away hand warmers end up too expensive if you spend a lot of time shooting in very cold weather and they don't get as warm either.
If you shoot in snow, you'll very quickly discover that your tripod legs sink in, especially into fresh powder. The simple solution is to make some little "snowshoes" to attach to the tripod legs. I made mine out of carbon fiber sheet (what else?) and they work perfectly and weigh nearly nothing. My G1028 tripod now also makes a nice trekking pole that doesn't sink into the snow. Any entrepeneurs out there are welcome to borrow my idea and make tripod snowshoes to sell. Just send me a set to beta test, eh?
Snow travelers are generally not in much agreement about snowshoes vs skis, but for photography snowshoes will be much more versatile and convenient, though under many circumstances skis are far easier for covering big distances. Then for photography verstatility you can carry snowshoes in a pack. I do strictly snowshoes because I generally go alone and snowshoes are much safer and more stable. A badly sprained or broken ankle in a remote area where nobody is likely to find you until you're a corpsicle can ruin your whole day. Slower and less skill demanding travel is also better to allow you to pay more attention to your surroundings for better receptivity to picture opportunities.
If you've never done shooting in serious mountain snow conditions, you have a big treat ahead of you if you can muster the courage to try it. The mustering took me decades and now I wish I had overcome my reluctance and fear sooner. I love the Sierra Nevada in summer and fall, but winter is an altogether different sort of magic and old familiar places become almost unrecognizable and can change a lot almost from day to day due to changing snow conditions. I'll be out almost every day for the rest of the season. With the record snowfall this year the snow season will last well into June above 10,000 feet or so.