we had a blast with our 5yo in Breckenridge! Most hotels there have programs set up for the kids, such as activities on the mountain as well as in the hotel like crafts, songs, stories etc. And the town is way too cute for words. There is usually snow there through March/April (it snowed through June last year!) and it has a lot of great toy shops, sleigh rides, trails, hiking, skiing is awesome, restaurants, indoor fun things. We love it.
The instructors for kids are amazing! My 5yo was skiing down the mountain (green trail of course) on her 2nd day!!!! I was a first timer, too, and my lessons were really great!
oh yeah, they do have snowmobile tours, horse back riding etc as well but we never got to that.
the bus system in town is really great too so you don't have to worry about a car/parking. it was very easy and took you to/from hotels etc.