While you'll want to wear mittens or gloves to keep your hands warm, they're not very good when you are ready to shoot. Look for mittens that can be folded back to bare your fingers or gloves with no fingertips. Keep your camera warm. Keep your camera inside your jacket, where it can benefit from your body heat, until you are ready to take photographs. Return it to the warmth of your jacket when you are finished.
Cold temperatures can zap the life out of batteries.
Regular alkaline batteries work better if they are very fresh. We found conflicting information about how well lithium batteries hold up in cold weather. Since originally compiling this information, my son used this premise for a science fair project. Keep spare batteries warm. Since cold temperatures play havoc on batteries, you'll always want to have a spare.