I love riding in winter. The horses are full of energy, overheating is not a problem, and there is all that arena time for months (enter mild sarcasm here). It is a perfect time to refocus after the summer months of leisure and decide what new goals to set. So here is an idea for homework: diversify your lateral work.
Do laterals through figures you would not ordinarily do. For example, ride a serpentine in haunches-in flexing your horse to the corresponding direction. Brush up on your literature (or talk to my dad) and know where all hooves should be falling on the ground. First rule is to design your figure well and ride it with forward motion, but not fast. Feel your horse, set the rhythm, and when all is well you should be able to open your fingers and let the horse move through you.
Be aware of your tendencies, such as unconsciously doing more work to one side than the other or always starting to one side first. Feel your body level in the saddle and stirrups, shoulders lining up over hips, knees over toes, head straight, and have one eye on your horse and one on where you're going. You can't correct what you're not aware of. Where do you rush? When do you give up? What muscles get tight? When does your horse resist you? Like my dad says, think well--do well.