Skiing started drawing people to Aspen just after Silver did. The Silver City has a long history of fostering the mountain fun it affords. Today the massive Aspen/Snowmass SkiCo operates its 4 mountains for a lot of visitors. Snowmass, Buttermilk, Highlands, and Aspen Mountain are located in different spots but your ticket gets you into all of them. See the Aspen Snowmass website for more about skiing. Aspen Snowmass hosts the X-games and tons of fun lessons, outings, and activities.
Aspen Expeditions Worldwide is the backcountry guiding service linked to the resort.
Sunlight Mountain Resort is a much smaller mountain up 4-mile road in Glenwood Springs.
Powderhorn is the ski area on the Grand Mesa just southeast of Palisade.
The Flattops and the Grand Mesa are more for cross country skiing and snowshoeing. This blog post is about backcountry skiing on the Grand Mesa near Mesa Creek. There is a lot of information about Mesa Creek here, but the important thing to note is you can enjoy the runs after you ascend 1000 ft, so go for this only if you are totally prepared and fit.