Here is a nice warm-up exercise that is helpful for your horse with too much energy in the cold, but also inspiring for a horse that gets tight through his back in the cold weather. Once you have walked long enough (sometimes power hand-walking can help the rider to warm up) and trotted enough to put your horse on the aids, try rising trot-canter transitions on a 20-meter circle.
Your goal is to first ride one circle in trot one in canter, then half circle in trot and half circle in canter, then a quarter circle in trot and quarter circle in canter. Try to be really accurate from point to point and ride the transition on the spot. Your horse will get more balanced in anticipation of each downward or upward transition. Your fresh horse will be able to let out some steam but has to keep thinking of your downward transition not to get out of hand, and your lazy horse has to think forward to the next upward transition. The rider's body will warm-up following the new rhythm of each gait and also with the challenge not to be left behind the movement.