Keep us updated on your plans. I've heard its doable on the dry winter years, but still an extreme climb.
I don't live close to Yosemite, but close enough to do daytrips to the park. I've done the Half Dome hike in the summer time, and have done a few winter time hikes on the valley floor. I actually prefer to visit during the winter and early spring time before the crowds get out of hand. I haven't done the Half Dome hike in years, but do the Mist Trail / Nevada Falls hike about every other year.
I hate Mist Trail, and will take longer John Muir trail on the way up. Mist Trail is okay coming down, but when wet (which it always seems to be) can be treacherous . It is basically staggered uneven steps cut out of granite rocks for long stretches. John Muir is more of a "horse trail" as is longer but a gradual climb. I would imagine both are covered in snow drifts at the moment. I think the gates leading to the John Muir trail will be closed, but that should be to keep the horses out. Just go around them.
We've been getting a lot of rain / snow this year in Northern California and the snow level changes daily. It might be 7000 feet one day, then drop to 3500 feet the next, so plan accordingly. The climbing cables will probably be frozen to the granite rock on Half Dome. And if you ask any Yosemite officials for input on this hike, they'll think you're crazy.
They probably won't stop you though. The park averages about 12-15 deaths a year, and the Mist Trail seems to cause a few of those.
Be careful.
I would also consider looking at some of the other hikes on the valley floor incase the Half Dome route is too snowy.