DURING ARRIVAL, THE PLT CHECKED IN WITH KNOXVILLE APCH CONTROL & STATED THAT HE WAS PROCEEDING TO THE DOWNTOWN ARPT FOR LANDING. AT THAT TIME, THE WX AT MCGHEE-TYSON ARPT (APRX 10 MI SSW) WAS CLEAR WITH 7 MI VISIBILITY. ABOUT 10 MIN LATER, THE PLT REPORTED THAT HE WAS ENCOUNTERING FOG IN THE VICINITY OF THE DOWNTOWN ARPT & 'MIGHT HAVE TO GO OVER TO MCGHEE-TYSON TO LAND.' A FEW MIN LATER, HE REPORTED THAT HE HAD EXECUTED A MISSED APCH FROM RWY 26 DUE TO FOG, BUT THAT HE SAW SOME LIGHTS & WAS GOING TO TRY TO LAND ON RWY 8. HE MADE A PROCEDURE TURN TO ALIGN THE ACFT TO THAT RWY. DURING THE 2ND APCH, HE ENCOUNTERED FOG AGAIN & INITIATED A GO-AROUND. SHORTLY AFTER THAT, THE LEFT WING HIT TREES & THE ACFT CRASHED IN THE RIVER NEXT TO THE ARPT. RESCUE PERSONNEL REPORTED THAT THE FOG WAS SO THICK THAT THEY HAD TROUBLE FINDING THEIR WAY ACROSS THE FIELD TO LOCATE THE WRECKAGE. THERE WAS EVIDENCE THAT THE LEFT WING BEGAN BURNING AFTER IT COLLIDED WITH THE TREES. THE TREES WERE LOCATED ALONG THE RIVER BANK NORTH OF RWY 8.