We do an annual ski trip over Thanksgiving to Colorado. So far, as long as we are willing to be flexible, we have had good luck, of course, this will only be our third year. There is a great article out there (I believe written by our own Tony Crocker) for determining best chances for early season snow. You can find it at http://www.skiingmag.com/skiing/trav...328639,00.html
Our limited experience:
Wolf Creek was 100% open during Thanksgiving 2004, but had next to nothing T-giving 2005. Because of that we changed our plans to Summit County. The elevations there are high and a few resorts open at least a couple of runs (Loveland, A-Basin). And since there are so many, we were able to choose which area to hit based on how much acreage was open. T-giving 2005 we skied Loveland, Keystone, Breckenridge, and Vail. Plenty of terrain was open, but we don't search for steeps, so were are probably easier to please than others. The great thing about Summit County is that even if you have no snow, there is still a lot to keep you busy, especially with Denver so close. We are scheduled for another trip to Summit County this T-giving with fingers crossed.
Of course, I haven't really helped at all about your question of the Little Cottonwood Canyons.