While digging a snow pit and pitching a tent in winter is great preparation for high-altitude mountaineering and a fun experience in its own right, Colorado has a better solution for winter overnights in the 10th Mountain Division Huts -- a series of backcountry huts that offer borderline decadent backcountry winter overnights. Some even have saunas.
Many of the huts fill up fast, and are booked months in advance. You can check hut availability at 10th Mountain Huts, but booking must be done by phone. Hut trips are a fun group activity; packing in a few six packs of beer, sitting outside on the deck and looking at the moon rise over the mountains covered in white can be a religious experience.
Shrine Mountain Inn is a great intro to hut trips. It is accessed from Vail Pass, and is only a a 2.7 mile ski or snowshoe from the parking lot. This is a popular hut for those looking to turn the classic Commando Run backcountry tour, an 18 mile ski from Vail Pass to Vail ski area, into a two-day trip instead of one long one.
The Inn consists of three separate cabins: Jay's, Chuck's, and Walter's. Each has its own propane stove and oven, and the three share a sauna. The three cabins can sleep a total of 36 people between them. A nice bonus is that all three have indoor flush toilets, so you don't have to trek out to an outhouse in the middle of the night.
For the backcountry skier, there is plenty of moderate terrain to access from Shrine Mountain Inn if you aren't doing the Commando Run.
Rates start at $30 per person per night. There is also a $6 U.S. Forest Service use fee that will be tacked on when making a reservation.