While en route from Saint Louis, MO (STL) to Aspen, CO (ASE), the aircrew encountered stronger headwinds than expected. They realized there would not be enough fuel reserved for an IFR flight to Aspen, so they elected to divert to Eagle, CO (EGE). However, their landing at Eagle was delayed due to a snowplough (with no radio) on the runway. After circling and re-entering final approach, the aircrew noted that the snowplough was still on the runway, headed in their direction. They continued their approach and the snowplough cleared the runway. A witness noted that the aircraft was still airborne when it passed the second turnoff, approx 2300 ft from the threshold. After touching down on the snow covered runway, the pilot deployed the spoilers and immediately applied braking action, but was unable to stop on the remaining runway. The aircraft continued off the end of the runway, went down a 15 ft bank and ran into a small ravine. The runway gradient was 1.4% downhill, elevation 6538 ft. The drag chute was not deployed. Cause: Proper touchdown point .. not attained .. pilot in command Contributing Factors: Weather condition .. unfavorable wind Terrain condition .. downhill Terrain condition .. ditch Weather condition .. high wind Airport facilities,runway/landing area condition .. snow covered Fluid,fuel .. low level Miscellaneous equipment .. not used .. pilot in command Airport facilities,runway/landing area condition .. downhill