Keep batteries and water close to your body to keep them warm. Batteries tend to drain fast in cold temperature and when not needed, put them in some inside pocket of your jacket.
Drink water! Dehydration in cold weather is as bad as in hot weather.
In winter the temperature is around -15C to -20C and might drop down to -30C, I wear multiple layers of clothes to keep me warm. Sometimes I have two pairs of gloves with me, one pair thats thin and can use to operate the camera and other pair is just a pair of thick mittens I can put on the thin ones. Two pairs of gloves keeps my fingers nice and warm.
If you need to change lenses, do it over a bag. With freezing fingers things might slip and fall, it's better for a lens to fall into a bag rather than snow. Best option is just not to change lenses.
Before you go from outside to inside (cold to warm) put your gear in the bag because condensation will form on the camera and lenses. Let them warm in the bag for some time, it's a way to prevent condensation from killing your camera. It works the other way also, going from warm to cold can be deadly for your camera, but the cure is the same.
And last but not least, try not to grab metal/aluminum(tripods) bare handed