If you're there while school is in session, the kids at Breckenridge elementary have a big hill they go sledding on behind their baseball diamond. Dunno how much sledding he'll be able to do with them after a day on the slopes because the sun goes down around 4:30PM there at that time of year. They have a playground too.
He's 4, so he shouldn't get that bored with you guys there if you bring some of his toys and the odd coloring book or DVD. There is plenty around that he'll enjoy seeing... all the christmas lights that are around, the horse drawn carriage in town, the stuff on the wall at the welcome center.