The situation is that there is no snow plowing service on this road. When the snow accumulation is sufficient to make it covered to some degree, the county puts up a "road closed" sign on the valley floor, perhaps about 1/2 way up. One can drive around the sign without difficulty, but one assumes their own risk for getting trapped, have an avalanche come down on them, getting themselves out. I don't believe AAA will go onto any closed road to pull someone out. So...you take your chances when you go past the sign.
Is it possible that it is open on Thanksgiving? Sure. Totally subject to the snowfall to that point.
G'luck!