I took my 3 children to Solitude to meet up with another friend, also with 3 kids, in Jan. 2007. The kids were ages 3 to 11. One thing all 6 kids enjoyed, in addition to the skiing, was the Olympic Park in Park City. If you choose to go, call ahead...we did, and we were able to see aerialists from Europe practicing. The athletes and coaches took the time to talk to the kids. It was an amazing site to see them practicing. And, their kindness was incredible. For us, we skied in the morning, and did the Olympic Park in the afternoon...it was plenty of time at the Park.
One SMALL reason not to rent a car is if the roads are horrible. I have heard of people getting snowed in because they were not confident of their winter driving skills, having to put chains on, etc. However, that is something you could deal with if the situation happens.
We had a great time on the entire trip...hope you do too!