I live in Georgetown. If you are going to drive the best place to go is to New Mexico, especially with 3 kids. I grew up in Colorado and it is a loooonnnggg drive with kids. We took our kids to Red River, New Mexico 2 years ago. Our youngest was 3 at the time. It was an easy drive. We stayed in a condo that had 2 bedrooms and a little kitchen and living room. It was great. Everyday the ski shuttle would come and pick us up and drop us off at the ski mountain. The ski school was wonderful. Both of my kids loved it. We put them in school for 2 days and on the 3rd day we went skiing with them. The mountain is really nice. There are also lots of other activities to do with kids. My older child went snow shoeing one day and had a blast. Let me know if you have any questions.
Also, the best place to ski in Colorado is Steamboat Springs.
Lisa