Cold air is heavy, therefore it creates more resistance to the flight of the ball. Cold, heavier winds naturally encourage golfers to swing harder, which will create more errors.
It will cause you to be out of position through impact, allowing your right side to dominate (for right golfers) at the inappropriate time. By having a more reckless swing to counteract the cooler weather, this action will move your right arm and shoulder out of the desired position. This will force the club head to approach the ball in a too steep angle. In golf talk: "coming over the top of the ball."
Because of the colder temperatures, all players should gear their swings to produce a lower trajectory to the flight of the ball. To accomplish this, the swing plane (path that the club travels) should be in a shallower arc. This will allow the club head to contact the ball properly. Also, play the ball slightly back in your stance.
One of the essential keys is to have your shoulders set up correctly at address. Having your shoulders in the proper position will encourage good shoulder motion throughout your swing. In the set-up (starting position), the right shoulder should be slightly lower than the left, with the right arm relaxed and the elbow gently tucked. From this position, the right allows the left to control the takeaway. Remember the left leads, and the right follows.
A very common error is that the right shoulder is too high through the hitting area. A simple, quick fix is to not allow your right shoulder to pass the ball. This will encourage you to come into the ball with more of an uppercut type blow (much like a boxer), as opposed to a roundhouse spinning motion that is too hard to time up consistently.
Also, when you're out there playing in this colder weather, protect your head, feet and hands. Try to keep your golf balls warm as well. Taking care of your equipment and yourself will make playing the game more enjoyable during this brief period of colder weather.
Tom Ward, PGA Tour Instructor