I think it's a hit-or-miss proposition with Brian Head. Last year they only had a few runs open late November to early December. We were thinking of driving up for Thanksgiving until we saw how limited the open terrain was. I'd just watch their website as your trip gets closer to see what the snow forecast is like. If they don't have most of the mountain open, I don't think it's worth the trip. Although if you have a free place to stay up there, the scenery is beautiful in that area and there are a couple of National Parks a stone's thow away.
Also, if you don't mind driving a couple of hours more, Mammoth could well be in full-swing around that time. It'd be a long, boring drive, but certainly a better skiing experience than BH.