The two peak seasons are Christmas-through-March (skiing) and late June-through-late August (music festival, hiking, summer weather). Within the ski season, the New Year week, Presidents' Day weekend, and the spring break weeks in February-March are the most crowded and expensive; January (after New Year) is comparatively quiet.
September is the local insiders' month. The crowds are gone, the weather is usually sunny and warm, and from about September 20 through October 5 the aspens above the valley turn brilliant gold — one of the great seasonal sights of the American West. Late April and May are the shoulder weeks when most ski lifts and many restaurants close; useful if you want a quiet visit but limited if you want to do much. The Independence Pass road opens around Memorial Day (late May) and closes by mid-November.