THE STUDENT PLT HAD FLOWN TO THE RIVERTON ARPT TO ATTEND A GROUND SCHOOL. REPORTEDLY, PRIOR TO HIS DEPARTURE AT APRX 2235 PDT, STARS WERE VISIBLE OVERHEAD, BUT THE HORIZONTAL VISIBILITY WAS POOR & THERE WAS A HAZE LAYER AT ABOUT 500 FT AGL. AT APRX 2250, A WITNESS NEAR THE CRASH SITE OBSERVED THE WHITE & GREEN LIGHTS OF THE ACFT JUST PRIOR TO IMPACT. HE REPORTED HEARING THE CONSTANT SOUND OF THE ENG BEFORE THE ACFT CRASHED. DUE TO DARKNESS & REDUCED VISIBILITY, THE WRECKAGE WAS NOT FOUND UNTIL THE NEXT DAY. AN INVESTIGATION REVEALED THAT THE ACFT HAD IMPACTED IN A RAVINE, SURROUNDED BY HIGH TERRAIN. IMPACT HAD OCCURRED IN A STEEP DESCENT WITH THE RIGHT WING DOWN. APRX 9 MI NORTHWEST OF THE CRASH SITE, THE WEATHER WAS REPORTEDLY OBSCURED, 2 MILE VISIBILITY WITH FOG, TEMP/DEW POINT 60 DEG, WIND 240 DEG AT 6 KTS. PRIOR TO THE FLT, THE STUDENT WAS CAUTIONED ABOUT FLYING IN REDUCED VISIBILITY, BUT HE RESPONDED, 'IT'S OK, I'VE GOT OVER 50 HRS.'