Key behaviours / activities to look out for this month are:
Most non-fawn bucks shed their antlers
New antlers start to grow
Deer spend a relatively large amount of time resting
Any bucks that did not cast their antlers last month, will most likely do so in December.
As mentioned in the section on November, the casting will be carried out in age order - oldest first. It's not uncommon for yearling bucks to get within a week of Christmas, before shedding their headgear.
Once the old antlers have been jettisoned and a scab has formed, the new growth will start straightaway.
For the deer that shed their old pair back in November, the new antlers' growth will be clearly visible from a distance by the end of this month. These are the males that will become the dominant bucks next year, and therefore possess a distinct advantage over the younger individuals, who started their antler growth later.
To understand why this is so, you might like to read the article called, "Why do mature bucks shed their antlers first?", which is located in the FAQ section.
In the winter, the deer try to minimise energy expenditure, and therefore they spend much of their time resting. So, December is a good time to try to make shots of them relaxing in a quiet spot.