I have hiked Half Dome in December on a dry year, and it was pretty simple. But it depends on where (and if) you encounter ice on the trail. I hiked it in May, 2011, as well. Here is the 2011 trip report and pictures: Half Dome with Cables Down
If the water level is low and the temps not too cold, the Mist Trail is ok, but it can get icy otherwise. The park may close a gate across the trail (the Mist Trail route) just past the main bridge below Vernal Fall. People go over the gate, but you're on your own if you do. The other route, the John Muir Trail, climbs switchbacks that are dry, bypassing the Mist Trail section. A branch from that trail descends to the upper Mist Trail route above Vernal Fall, and should be dry and accessible (unless after a heavy snow.)
There is a section on the JMT after the branch that can ice up and be treacherous, too, worse than the Mist Trail. So descending to the upper Mist Trail would be safest. From that point, climbing the trail on the north side of Nevada Falls would be the safest and driest.
Once above Nevada Falls, there is only one trail, and the only trouble on it would be whatever the accumulation of snow there is. If there is heavy snow by December, you will have to tramp through it. Due to the trail's popularity, there will likely be a boot track.
Once you get to the sub-dome, the shoulder can be steep. Crampons might be helpful at that point, if there is an accumulation of snow. (If you call the Yosemite N.P. wilderness trail number, they can tell you how much snow there is. But beware, they will warn you not to hike, since they have to do that for the most inexperienced hikers and callers.) When we hiked in May, the snow was consolidated and was not much trouble at all. December snow would be less consolidated.
The cables are down, meaning the poles have been removed that hold the cables up at elbow height. The cables are still there, just lying on the granite. All you do is pick the cable up and climb. The weight of the cables actually gives you better traction. Do NOT go up the cables if the rock is wet -- it can get slippery. Do not go up if there is a storm, or lightning possible. If it is dry and without ice, the cables are great fun.
On the cables, I like to go up without gloves -- skin grips the cables better. (Except if the steel is too cold!) On the way down, leather gloves enable you to slide the cable through your hands as you go down, and you can squeeze tighter to brake and slow, or relax the grip to go faster. Fun!!
If you take crampons, those icy sections of the Mist Trail and JMT would not be any trouble with the crampons.
If you go, post a report!