Best chances of early-season snow (Christmas) will be to go out West.
If you've got family members who aren't gung-ho skiers, I second the Aspen/Snowmass suggestion. Another option: Salt Lake City or Park City. Lots of stuff to do off the slopes for those who don't want to ski all the time. And, of course, some of the best skiing anywhere, with as-good-as-it-gets guarantee of good...or great...snow in early season. If you want a historical town, stay in Park City, which also is beautiful at Christmas. Believe me, your Mom would LOVE Park City. Park City lodging comes with an interchangeable ticket to Park City resorts, but it's not valid during Christmas when you plan to be there, so figure out where you want to ski and see if you can pre-purchase online for discounts. If you stay in Salt Lake City you can get a lodging deal that has an interchangeable ticket for the four Cottonwood Canyon resorts (very cheap, $42 a day for tix, not sure if there are blackout dates or not).
If you want good snow in the East, I'd stick to as far north as possible, such as Stowe or Sugarloaf. Yes, Killington will make snow, but they might not have the natural stuff with it, and everyone goes to Killington because it's so close to the metropolitan areas. The farther away from cities the better as far as crowd control and chances of good snow. Stowe or Sugarbush will be good places for the non-ski activities, plus they have good beginner terrain. Also both towns are beautiful at Christmas time. Sunday River has better beginner terrain than Sugarloaf but will be more crowded. not as much to do off the slopes at either Maine resort, though. New Hampshire tends to be dicey for early snow.
For your March trip: I LOVED Mt. Baldy, my favorite place when I lived in L.A. Very funky, as already described, but character up the yazoo. If other family members are going with you, Big Bear is probably better though.