You can rent a car from at least five different companies at Aspen's airport.
In summer the 160-mile, three-hour drive from Denver to Aspen is a delightful journey up the I–70 corridor and across the Continental Divide through the Eisenhower Tunnel (or by way of the slower, but more spectacular, Loveland Pass), down along the eastern ramparts of the Collegiate Peaks along State Highway 91 and U.S. Highway 24, with a final push on twisty State Highway 82 up and over 12,095-foot Independence Pass.
The scenery, particularly south of Leadville on U.S. 24, is among the best in Colorado, with views to the west of 14,433-foot Mount Elbert, the highest mountain in the state. Independence Pass is closed in winter (the timing depends on snowfall, typically late October–late May), but motorists should always drive cautiously. Blinding snowstorms—even in July—can erase visibility and make the pass treacherously icy. Be especially careful on the western side, where the road narrows and vertigo-inducing drop-offs plunge thousands of feet from hairpin curves. Both Route 82 and I–70, like all Colorado roads, should be driven with caution, especially at night when elk, bighorn sheep, and mule deer cross without warning.
Generally speaking, driving to Aspen from Denver in winter is more trouble than it's worth, unless you plan to stop along the way. The drive west on I–70 and east on Route 82 takes more than three hours at best, depending on weather conditions and, increasingly, ski traffic. On the other hand, the 3-mile drive from the Aspen/Pitkin County Airport (ASE) is a breeze along the flat valley floor. The 70-mile drive from the Eagle County Airport (EGE)—which doesn't cross any mountain passes—is another option. Whenever you visit, the traffic and parking may try your patience.