New Years is one of the most perfect times for you to go hard on your marketing and enroll new students.
Adults and children are making resolutions and setting goals for the new year and that almost always includes fitness (getting healthier, getting in shape, losing weight, etc).
You should have multiple marketing methods firing at all times - social media, google, rack cards in local businesses, EDDM sent to people in your area, VIP cards, promo booths, buddy passes, all of it.
You can start your New Years marketing now and continue for the first couple months of the year. You have plenty of time to get things rolling!!