We always fly to EGE these days, never DEN. Agree with what everyone else has said.
Additionally, closures of Vail Pass and Eisenhower Tunnel can cause big problems for rental car operators at DEN. One year, we waited over 4 hours to pick up our rental car at Avis DEN because their cars were all stuck west of the tunnel due to road closures.
Do yourself a favor and fly to EGE.