This will be the first Christmas in over 15 years that we didn't spend in Yosemite Valley, so I can offer you some suggestions from past years. I assume that you are talking about day trips. If you are asking about overnight trips into the back country, that's another topic. I prefer to do those in the Spring, when the days are longer and the weather more suitable.
My first comment is that you cannot plan what to do very far in advance, because the weather is all over the map. At Christmas of 1996, there was deep snow everywhere, even in the Valley. A week later came a warm typhoon rain, a real gully-washer, which caused the worst flood in a hundred years. If there had been a normal amount of snow, it wouldn't have been nearly so bad...
Another year, there was no snow in the Valley. Badger Pass Ski Area was barely open. You could just walk to Dewey Point in your hiking boots. Every trail in the valley, and hiking up the sunny side up to the valley rim, was in fine hiking shape.
Usually, at Christmas there is little or snow on the sunny side of the valley, but there is some snow in the woods and on the shady side. You are likely to see snow or rain fall while you are there. The main problem on the valley trails will be refrozen snow, which can be rough and icy and hard to walk on. Usually Badger Pass is open for downhill skiing, and the cross country center has groomed a trail all the way to Glacier Point. They even offer (through the ski school) overnight bunks there, which is a really good deal if you don't like to ski with a heavy pack. Usually there are lot of unpacked trails in the woods, where you follow existing tracks or you can break trail yourself. The main down side to the latter is that you are likely to meet a bunch of snowshoers on the way back, who are happily obliterating the ski track that you just laid.
Four Mile Trail is always closed; there are some avalanche chutes that it crosses near the top. The Mist Trail is almost always closed. The John Muir Trail is usually open, as is the Yosemite Falls Trail, but both are subject to closure due to falling ice. Hard to predict. The Snow Creek Trail has always been open, in my experience. It is one of the main routes from the Valley to the winter hut in Tuolumne Valley. Of course, you will have to switch to skis at some point on the way up.
I have quit bringing snowshoes. Too clumsy on the trails. For bumpy re-frozen snow I wear small instep crampons on my boots. I understand that yaktrax are more versatile, especially if you are on the Yosemite Falls Trail, going from frozen ruts to bare trail to re-frozen snow, to bare trail, changing every hundred feet. But I don't own a pair of yaktrax. In any case, if you have just hiking boots, you are going to have to be very, very careful when crossing the icy re-frozen footprints on the trail. If you post-hole to the knee more than a dozen times, turn around and try another trail. You are really going to hurt yourself if you continue post-holing among the granite blocks and steps that abound on trails leading up from the Valley.
If you like hiking, don't overlook some of the lower trails that may be clear when other stuff is snow-filled. The former Coulterville Road and the lower part of the Old Big Oak Flat Road are fine hikes when others are too snowy. The road up to the fire tower by route 120 is a good hike or cross country ski route, depending on the conditions, as are the forest service roads above Foresta and the paths through the various redwood groves.
There are a lot of forum postings about the old roads. Here are a couple:
http://yosemitenews.info/forum/read.php?3,26668http://yosemitenews.info/forum/read.php?3,26509,26509#msg-26509and here is one about some cross country trail breaking near Badger Pass:
http://yosemitenews.info/forum/read.php?3,30738,30738#msg-30738