I haven't skied Crested Butte but have heard from friends that it's nice. One caveat: not sure they make snow, so check on that and the usual first opening to make sure it's likely they'll be open. I would think probably (esp if the El Nino predictions come true for the southern mtns to get good snow this year) but obviously better to check than arrive at a mountain covered with 6" of snow.
If you or anyone is hell bent on Summit County, CO resorts, IMO Arapahoe Basin and Loveland Ski Area are usually better priced and *always* have snow, usually by late November. Those are the two that compete to see who opens first, so there will be snow in December. The nice thing about A-Basin is that they have a beginner-only lift (or at least they used to) called Goose something. If you are planning to teach kiddos yourself, a resort with a beginner-only ticket option is great. I taught my sister to snowboard at A-Basin, and at the time it was like $7 for a beginner lift ticket. Good thing too, b/c my mom fell and broke her shoulder on the first run after lunch, so a half-day was all we did. The negative with A-Basin is no town at the base, but you'd be better off finding a deal in Dillon or Frisco for lodging anyway. Loveland Ski Area (not to be confused with Loveland Pass, which is the alternative drive over the mountains that bypasses I-70, or with the City of Loveland, which is on the Front Range between Longmont (MMM's city) and Fort Collins) may have a beginner-only hill but it's got sort of two areas which could be nice: a green-blue area with short runs (below timberline) and a blue-black area with long runs that go way above timberline. The wind can be brutal, so much so that the big run area has "escapes" halfway up (at least some years ago when I went there). The easier terrain area tends to be a little out of the wind though.
Keystone has kind of crappy snow, IMO, though they do make it so it will be open in Dec. Vail is terrible in my opinion...but it's a huge mountain so if you venture farther out you have smaller lines. I have only ever skied there for free or super-cheap (friends who worked at resorts, etc) but would never pay much to go there. Also there's no free parking at all in town. Copper Mountain and Breckinridge are both pretty good-cheaper than Vail with at least as good experiences, and both closer to Denver. However, more expensive than necessary for teaching kids to ski, unless a very good combo lodging/lift ticket can be found. Unlikely at Christmas time.
As for skiing in April, as someone was asking: early April is fantastic! It's usually sunny, sometimes above freezing, the light lasts longer in the day so it feels nicer and the snow is soft. If it does snow, it's often at night for some reason. It's also ideal if you don't want to get up and at 'em right when the lifts open: usually the snow is great by 10am. The crowds have thinned out since everyone is now watching baseball or some such, and prices are accordingly cheaper. If you're not bound by employer schedule or school schedule, early April is about the best time possible to plan a ski trip to CO. Often I've seen 3days for <$100 deals, or really good lodging/ski combo deals in April. I would think further north would be similar or even better, but further south (NM, AZ, etc) may be dicey if they don't routinely have snow last til April. Some CO resorts are open later (A-Basin is usually late April and occasionally makes it way into June) but some must close due to wildlife considerations and the snow gets less reliable after tax day.