According to the Colorado State University Extension page on West Nile Virus:
Mosquitos can live at least to 10,000 feet:
Culex tarsalis, one of the main West Nile virus vectors, commonly occurs up to altitudes of 8,500 feet and is found as high as 10,000 feet above sea level. Other potential vectors are more common above 8,500 feet and can be found well above this elevation. On the other hand, the transmission season becomes shorter as elevation increases, which probably reduces risk significantly. Given the lack of knowledge and experience with this disease in Colorado, it is prudent to use an effective repellent when mosquitoes are active, even at these higher elevations.
Yes, they do.
Elevation in feet for Avon Colorado is 7,430 feet
5280 feet above sea level
Keystone, Colorado is 9,173 feet (2,796 meters) above sea level
Granby, Colorado is 7,935 feet (2,428 meters) above sea level
The elevation of Evergreen, Colorado is 7,220 feet (2,200.6 meters) above sea level