Drive if you are already in the region
Northeast to Vermont: drive. Front Range to Summit County or Winter Park: drive, but not Friday at 4. Wasatch locals: you know. Everyone else is pretending a 12-hour winter drive with three kids is cheaper. Count hotel nights, meals, and the day you lose on each end.
Fly to Salt Lake if you can
This is not Utah boosterism, it is arithmetic. SLC to the mountain is 30–45 minutes. DEN to Breck is two hours on a good day. RNO to Heavenly is about 75 minutes plus weather. The airport is part of the resort.
Gear on planes
We ship skis. Airline ski-bag fees plus the circus of a terminal with kids is a tax we stopped paying. Boots can come as carry-on if you are stubborn; they are also heavy and annoying. Helmets in a duffel.