A good pair of woolen gloves or down-filled ski mittens are a must for keeping your hands warm. Remember, your hands are the only part of your body in contact with the club. Lose the feeling in your hands and you'll never swing well. Keep your gloves on at all times during the round - except when playing your shot. A cold ball flies a shorter distance than a warm ball.
Balls fly shorter distances through cold air than through warm air.
Taken together, these two factors could well see you using two more clubs for the same distance through he air in winter as compared to a warm, summer day. The sub-surface of greens becomes solid making the greens lose any 'give'. You'll have to consider dropping your approach shots short of the pin - or even short of the greens. Your ball will react to frozen patches of ground as if they were concrete. Around the greens you can forget opening the club face and playing high-spin, cutup shots.