THE CERTIFICATED PRIVATE PILOT WAS ON A CROSS COUNTRY FLIGHT THAT BEGAN AT ABOUT 0830 HOURS AND WAS PLANNED TO COVER ABOUT 1,300 NAUTICAL MILES. THE PILOT DEPARTED HIS LAST FUEL STOP AT ABOUT 2000 HOURS WHERE A WITNESS REPORTED THAT THE PILOT APPEARED FATIGUED. THE ROUTE OF FLIGHT WAS OVER HIGH MOUNTAINOUS TERRAIN THAT HAD A MINIMUM FLIGHT ELEVATION OF 13,500 FEET. AN EMERGENCY LOCATOR TRANSMITTER SIGNAL WAS RECEIVED AT 0024 HOURS, LOCATED 105 MILES WEST OF THE LAST DEPARTURE AIRPORT. THE AIRPLANE WAS LOCATED BY SEARCH PERSONNEL AT 11,000 FEET AND HAD IMPACTED A MOUNTAIN SIDE IN A REMOTE AREA OF DEEP SNOW. AT THE ACCIDENT LOCATION, THE AIRPLANE WAS ABOUT 1,000 FEET BELOW THE MOUNTAIN RIDGE LINE. THE TIME AND LOCATION OF THE ACCIDENT PLACED THE AIRPLANE IN AN AREA THAT DID NOT HAVE ANY GROUND OR MOON ILLUMINATION.