December is the first month in the beekeeping season you actually get to relax a bit. With that being said, there are still a few beekeeping tasks you will likely need to complete, especially if you’re in the Pacific Northwest.
What our winters are like

Where I live, in Eastern Washington, close to the top of a pass, we have harsh winters. Usually we get snow the end of October or early November. The snow really starts to pile up around December, where we can easily get up to three feet. Temps hover around 20 degrees during the day and drop to the mid to low teens at night. Then in January, it’s not uncommon for us to get a cold snap where temps plummet to around 0 degrees during the day, and as low as -20 at night. It never truly does get warm for about two weeks. February begins to warm back up, with temperatures reaching the mid 20s again during the day, and as low as roughly 15 degrees at night.
What to do in December

December is the time when snow really accumulates, here in the Pacific Northwest, so it is important to ensure entrances stay open. Your bees may propolize upper entrances, so don’t rely on these. Snow can build up around the rest of your hive since it acts as insulation.
Also, clear dead bees from the entrances, so the bees have access to them.
Beyond the “regular” tasks like ensuring the lids didn’t blow off or the hive get tipped over, this is the main task.
If you use oxcilic acid vapor, consider a wintertime application, administered in such a way as to not open the hive. (One would not normally open a hive for an OAV treatment, but it’s especially important to avoid opening the hives unnecessarily this time of year to prevent chilling the bees.)
Beyond this, make plans for next year. Find and order resources, get catalogs coming in the mail, and repair damaged equipment. If you are ordering bees, begin finding a supplier.
December is a good time to get others into beekeeping as well. With the holidays coming up, consider getting a beekeeping kit for someone who’s been talking about the hobby, or a bee barn for someone who likes the idea of more pollinators but doesn’t want to keep honeybees.
Enjoy the break
Overall, this time of year, take a break. If that means taking only a break from being directly in the hive that’s great, keep learning all you can. See some of my favorite resources here. If you just want to step back and completely take a break (besides keeping entrances clear) that’s alright too. Just make sure to take the time to avoid beekeeper burnout. Enjoy this time!

For more winter beekeeping advice, see these relevant articles:
January Beekeeping in the Pacific Northwest
February Beekeeping in the Pacific Northwest
How to Tell if Your Hive Is Alive in the Winter Without Opening It