Now that the rut is over, big bucks are looking for food. They've likely run off 20% of their body weight chasing does, so their full attention is now on survival. That means food and cover, and with the added pressure from the gun seasons and hunter activity, big bucks aren't going to give you the same opportunities they did in September or October.
Some tips for bow hunting, late season:
First and foremost, dress the part. You're going to need several layers, and a great base layer. Don't totally bundle up before you walk out, though. Save your heavy, outer layer for when you get to the stand so you don't sweat, then freeze. If you get cold after an hour, and have to come in, it'll defeat the purpose of your hunt. I always dress with the hope of sitting for at least 3 hours. In late December, that can be a challenge, but it's always my goal.
Assess your property, again: Bow hunting in late December is going to be different that September, for obvious reasons, so sitting your early season bow stands might not work now. With the recent pressure, big bucks will be looking to take direct routes from cover to food, and it may not be that far of a trip. Figure out which of your food sources will be most attractive to the bucks in your area. If there is great cover, and it's close to the food, then find a way to hunt that source.
You don't have to hunt at 5am. A lot of big bucks have been shot between 11am and 2pm. While I was scouting last week, I saw a great 8 pointer and several does hanging in my field at noon. Another day, I got a nice 10 on camera in the same field in the noon hour. Deer are moving during the day, so sleep in, then go get 'em.
Acorns are your friend. If you had a spot where a lot of acorns fell this fall, get back in their and hunt over that spot. As it gets colder and the food gets more scarce, the big bucks will be back at those acorn spots digging for any leftovers.
Swamps can be interesting. My best 'honey hole', where I see the biggest bucks, is the part of my land that is 30 acres of hard woods and swamp. Right after the swamp freezes, it becomes the worst spot to hunt because of the slippery ice, but once it's covered in snow, the deer like to move back in there because the cover is amazing. Watch your step, but get back into the swamp to score.