Well, New Year's Eve is on a Sunday night this year. As a result, most people, including students, will be back in the swing of things by Jan 5th. You're good to go. I'm not sure what terrain you're expecting to ski, but it won't be too busy compared to the rest of the season. Teacup won't have too long of a lift line.
BC won't have any crowds. You won't wait in line at all. I like skiing the glades around Bachelors Gulch and I think early January will be a playground there.
By the way, I spent some time today at 11,000'. The snowpack is surprisingly good right now. It seems to be setting up for a great early season and Vail's back bowls are really going to benefit. About 30 - 40" of snow between now and the end of November will put Vail on target for an opening of bowls shortly after Thanksgiving.