I would think of all the places surrounding SLC, that Solitude would be amongst the least crowded. There are also several good "generic" reasons that it may not be all that busy Christmas week.
In general many major ski areas see an influx of folks when the kids are out of school but there are typical trends that hit the areas. In Solitude's case you might see some larger than usual traffic the Saturday before Christmas if the snow is good but that probably won't be the case on Sunday.
Don't expect things to be too busy leading up to Christmas and the 26th (maybe some local traffic). Most that are headed from longer distances use the 26th as a travel day. Then the poop hits the fan 'till mid-day New Years Eve at the latest. New Years day should be slow.
Odds are if there is not significant snow there, let's say before 12/15 you should expect less crowds. If there is a major dump while you are there (or series of significant snows) the locals will come out.
That's the usual for most areas. Solitude is quieter than most areas, and Powder Mt. would be another spot that may not get inundated with skiers. Mid-week / pre Christmas Snowbasin should work too.