Are you skiing on Sunday? I assumed travel day, start on Monday. Either way, it's only a couple of days, follow the advice about going to Solitude or somewhere else (if you decide on UT).
As you already seem to know, the crowds aren't so much about the locals as the tourists. That's why big destination resorts are the most crowded and that's why the busiest week tends to be the holiday week - when people from around the country are traveling to ski resorts. So I don't think the Mormons will have a huge impact one way or the other, especially not considering a lot of other locals (and travelers, for that matter) are exactly the types that will be drinking and partying and probably only go out if it's a big powder day (in which case Bird will be crowded no matter what).
I seriously doubt that a significant number of people are taking a short week. If that were the case, the X-Mas to New Year's week wouldn't be all that crowded to begin with because people could plan to take New Year's to the 7th off instead (it's not like this is the only year you'd have a shorter work week). Wednesday through Friday really isn't that short of week, anyway, especially if you're already taking the holiday week off.
Snow is hit or miss in early January. All four seasons I've been here, early January has been the driest part of the season. Typically it doesn't pick up until the last week or two of the month. December can be good or it can be crap; this year was the latter. Not the best time if you're really looking for prime, powdery conditions, but that's going to be a question mark no matter where you plan this far in advance.