The last 2-3 years they've quit taking winter reservations, and I was worried at first, but have never had any problem with site availability. However, I've never gone up camping the week after Christmas, so I really can't say "absolutely not, no worry!". As demand lessens, they close the loops further up, and they always seem to have plenty.
With this current storm, and a predicted one next week, the campground will be pretty damp and cold, which will keep most people away. I'd suggest bringing a snowshovel if you have one. They do clear them out when heavy snow hits, but it takes a while, and you may want to improve on their work...
I'm a tent camper and when I go up in midwinter and hit a snowstorm, I usually chicken out and head to Mariposa or Oakhurst, and drive in for the daytime (the lodge always seems to double its prices for some reason). But a trailer should give you a warm dry refuge. And if you wake up after a snowy night, there's nothing like an early morning valley walk with fresh snow. Enjoy your trip. Bring chains.
Gary
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