Can I just take an Uber from Denver Airport to Vail?

You often can, and in winter there are plenty of drivers working the valley — including local limo and car-service operators who switch the app on between their own bookings. So this is not a question of whether Uber exists here; it does. It is a question of what you are relying on. A rideshare trip is confirmed when a driver accepts it, and a hundred-mile run into the mountains is a long commitment for a driver with no guaranteed fare back, so acceptance is less certain at the times you most need it — late arrivals, storm days, holiday weekends. Fares also move with demand, which is exactly when you are travelling. Shoulder season and summer see far fewer drivers in the valley than a February Saturday. If a car not showing up would cost you a flight or leave a family standing outside at 11pm with ski bags, book a vehicle that is committed to you. If your plans are flexible, Uber is a reasonable way to move around the valley.