colorado is a great option!
What part of the spring season are you talking about? April and May are my favorites for big mountain backcountry, but hut trips are usually better in Feb. and March. 10th mountain huts are great, but don't forget about the San Juan huts, Hinsdale Route Huts, or the Alfred A. Braun huts. There are some fantastic options out there, however booking one at this point in the season can be difficult - they are relatively popular. Any of the main mountain passes are good places to start for car supported backcountry. Wolf Creek Pass, Monarch Pass, Freemont Pass, Loveland Pass, and Berthoud Pass all have fantastic turns available a short walk from the parking lot. Hope this helps, have fun!