The flight departed without a flight plan or weather brief. En route, deteriorating weather was encountered and an IFR flight plan was filed to a revised destination. Clearance was received for a VOR approach and the pilot was advised of 1/2 mile visibility in snow and fog. A missed approach was reported over the UNICOM frequency. Impact occurred with a heading of about 170 degrees at 7,700 feet MSL in mountainous terrain on the 173 degree radial, 7.3 miles from the VOR. The inbound course to the final approach fix was 170 degrees with an inbound final approach course of 196 degrees. Airport elevation was 5,914 feet MSL. The airport was located on the 196 degree radial, 5.5 miles from the VOR final approach fix. The VOR approach to runway 21 called for a missed approach to be executed at 5.5 DME from the VOR and a minimum descent altitude of 6,600 feet.