Your best bets for December will be hikes from Yosemite Valley. The trails are typically snow-free to about 6000-6500' unless there was a recent cold storm. Going higher than that may require snowshoes to avoid endless postholing. Some good mosty snow-free trails are:
- Yosemite Falls trail to the top of the falls, then continue to Yosemite Point or Eagle Peak
- Snow Creek trail to the large flat area at about 6500', which has good views of Half Dome, Clouds Rest, and Tenaya Canyon
- The Mist/JMT trail to Little Yosemite Valley Depending on conditions you may need to take the Winter Route--there will be signs and gates to keep you away from potentially dangerous areas (the Vernal Mist Trail and the JMT above Clark Point). You could continue towards Half Dome (the shoulder makes a nice and safe destination) or Panorama Point from here to make a long day.
- The Four Mile Trail to Union Point. To answer your question: The trail crosses some dangerous avalanche zones, especially just past Union Point and just below Glacier Point. Depending on how much snow there is, the danger could just be that the trail is icy/slippery or that there's a danger of avalanche due to recent heavy snow. Sometimes you'll see many footprints heading past the closed gates...
There are many off-trail scrambles in the valley that have been discussed on this forum, but most of them are much more dangerous in winter due to ice and snow.
For all these trails I'd recommend ice traction devices (such as Kathoola micro-spikes) since you will could encounter ice along the trails even if they are open and mostly snow-free.
If there isn't much snow or if you are OK with walking several miles in snowshoes, you might consider some nice longer semi-loops (all in the 14-18 mile range):
- Up Snow Creek, across to Yosemite Falls via North Dome, then down to the Valley via Yosemite Falls
- Up the Four Mile Trail (if passable) then down to Happy Isles via the Panorama Trail
- Up the Old Big Oak Flat Road Trail, across the top of El Cap, past (over?) Eagle Peak, then down Yosemite Falls
All of the above have been done by people on this forum and there should be trip reports--even with winter conditions.
Outside the valley:
- The Old Big Oak Flat Road trail leads to the top of El Capitan--a long day hike, but there are nice views short of El Cap, and this trail doesn't get as much traffic as the other trails.
- The trail to Rancheria Falls in the Hetch Hetchy area is usually snow-free and makes for a nice 12-ish mile out-and-back
- If there is a good bit of snow both the Merced and Tuolumne Sequoia Groves can be quite nice, but short, strolls.
December may be a bit early for there to be much snow for skiing, but if we do get lucky, there are several excellent ski and snowshoe routes out of the Badger Pass area. I'd recommend Dewey Point if you're OK with backcountry skiing or snowshoeing, or taking the Glacier Point road to at least "Clark View" (just past the Mono Meadow trailhead) if you just want to crank along in groomed tracks. Badger Pass rents cross-country skis and shoes; they also have a small-ish downhill ski area. And out and back to Glacier Point makes for a long day, but you can get overnight accommodations at the ski lodge at Glacier Point if it's in operation.
El Capitan, Eagle Peak, and North Dome are probably your best bets for "peaks" in winter. A strong hiker could probably do Clouds Rest in a day from the valley. With proper mountaineering gear you could of course go anywhere, but that would camping overnight in the backcountry. The days in December will be short--maybe 9-10 hours of sun, but of course less if you are in a valley or canyon. This may limit your ability to do some of the longer day trips here--it will generally be below freezing if the sun isn't up.
Keep an eye on this forum for updates as winter approaches, and let us know how your trip goes!