I suspect that we can all agree that it's not the ideal time to travel for a ski vacation, but family, school and work schedules all dictate the plan. And, truth be told, it is most often still an awful lot of fun! Not optimal? Sure. Taking some chance on the amount of snow? To some degree, sure. And paying the top dollar prices for ANY destination resort? Yes.
My recommendation would be to think about the type of vacation that you want, and I assume that consideration to the budget {if any} comes into play. I'm guessing that this may not be a "budget" trip, but then again, very few of us like to throw money away.
One of the considerations was no more than a 1-2 hour drive from the nearest airport to the destination. I have the two usual "suspects" on my recommended list. One is Aspen. I have had family in Aspen for a long time, and it's the least crowded iconic ski town/areas in the country. Even during one of the busiest weeks of the year, crowds will still be manageable. Skiing will be good. Not as good as early March, but very good. Everywhere you go, and everything you do {for the most part....you can get some local knowledge if you like} will be expensive.
You can fly right into Aspen, but you'll want to get on that now to lock up fares, or to see if you can use miles. Otherwise, you need to drive up from DIA {or be driven, again thinking budget/no budget} and that's more than two hours.
Deer Valley is logistically easy. Fly direct to SLC, and it's inside your timeline to the door. The limited ticket sales will make DV less busy than some of the other areas, and during this week, that could be a huge factor. In taking the liberty of guessing that this may not be a budget trip, I think that Deer Valley fits, and yes, you can visit some other areas nearby if you want to. Or you can just have a very relaxing experience at DV.
I'd personally limit it to those two. We can open it up form there, but you're taking chances with snow, and potentially with crowds. One other potential for me would be Sun Valley. They might be lean on natural snow, but they make a TON of snow, and they buff the majority of the place. If one likes to cruise fast on groomers of any kind of steepness, it's tremendous. And the town is just a classic.
I have been skiing my whole life, and we have never travelled over the holiday, other than to be with family at their ski homes. When we are home, we ski early and stop when the crowds get big {unless the skiing is phenomenal, which it rarely is....}. Then maybe snowshoe, or watch a movie. Take the dogs on longer walks, etc. The ski experience is often not that great. Over the last five seasons, I have been in Aspen, Steamboat and Vail over that week. Aspen, by far, would be my pick.
Another thing to keeping mind, in terms of crowds is that 12/23-12/26 tend to be the lightest, everywhere. Then each day tends to get incrementally busier, with New Year's Eve being the busiest. Then things tend to get less busy, depending on how the calendar falls. 1/1 is a Monday this year. Probably will be a travel day for most.
My vote is Aspen with DV a very close #2. There are also destinations with minimal crowds that others have mentioned. Just don't know how the OP and family would view them as a destination trip.
Good luck......Good "problem" to have!
Couple of options in the East, but I don't think that are under consideration. Not sure if I'd pick Jay at Christmas.
And my go-to's are a risk for a number of reasons. Crowds, snow, etc.
.
