The best way to see Bryce is at sunrise. And that, of course, means being there very early. So you'd either have to stay over the night before, or leave Las Vegas in the middle of the night. Better to plan a full-on Bryce and Zion trip at another time. Easy to tie it in with a visit to the North Rim of the Grand Canyon, too, which is right along the same road (more or less) but is closed in Winter.
I doubt you'd need a 4WD vehicle in Zion in December unless you really plan to take to the back roads - and there aren't really any inside the Park. There are two roads through Zion. The main Highway 9, that runs from the West Entrance to the East Entrance and beyond, and the road that runs along Zion Canyon to Zion Park Lodge. If you'll be there Christmas Week, as was posted above, the Zion Canyon Road is closed to vehicle traffic, and you'd have to ride the Park Shuttle. So the only road you'd be driving on is the main highway, which is busy enough the be clear 99% of the time. The only thing that might be an issue is ice on the corner switchbacks as the road climbs up toward the Zion-Mt. Carmel Tunnel. But even that is doubtful - if the Park is open to traffic, the roads will be tended.
See this image from Google Maps:
If I was going to Zion for my first visit, I'd rather go at a different time of year, when the trails and lookouts will for sure be open. Spring and Fall are great there - Summer gets a bit hot, and very, very crowded. In Winter, you're dealing with a lot of variables you can't control. Places and things you might want to see and do otherwise may not be accessible. So other than a few photo ops with snow on the ground and on the hilltops, there isn't a huge reason to go so far out of the way to see Zion right then.
For the time you'll have in Las Vegas that week, why not check out places that are much closer to get to, are a lot less crowded, and that are just as scenic: For example, Valley of Fire State Park is amazing, and will be much more easily reached. http://parks.nv.gov/parks/valley-of-fire
There is a back road from Las Vegas that runs right past the Park that has great scenery along the way. The Valley of Fire Scenic Byway is a great road to take. https://travelnevada.com/tours-cruises/valley-of-fire-scenic-byway/