Will they ski?
Some 3-year-olds take private lessons and love it. Many 2-year-olds should be in care or a sled. Private-lesson minimums are often 3; group is often 4. Smugglers' and Steamboat are built for the younger edge. Do not talk yourself into Alta.
Care is the trip
Licensed on-mountain daycare is a finite resource. Steamboat, Smugglers' Treasures, Deer Valley Children's Center, Keystone, Park City — these have it. Brighton and Alta do not. If care is full, you are tag-teaming. Tag-teaming can still be a good trip. It is not the trip in the brochure.
Altitude and sleep
Summit County bases sit near 9,000–9,600 feet. Park City and Steamboat are kinder. Vermont is kinder still. Fly-in, ski-afternoon, skipped nap is how you spend $400 on a day nobody remembers fondly. Pediatrician first if your child is under 2.