BEFORE TAKEOFF, THE PLT OBTAINED WX INFO. NO WX RPRT WAS AVAILABLE FOR THE DEP ARPT, BUT THE DESTN (HARTFORD, CT) WAS RPRTD AS CLEAR. THE PLT SAID HE WAS INFORMED ON UNICOM FREQ THAT THERE WAS ONLY GROUND FOG IN RHODE ISLAND, WHICH SHOULDNOT HAVE INTERFERED WITH HIS FLT TO HARTFORD. AFTER PREFLIGHTING THE ACFT, HE 'OBSERVED THE STARS DIRECTLY OVERHEAD AND CONCLUDED THAT THERE WAS JUST GROUND FOG.' ALSO, THE PLT STATED THAT AFTER TAKEOFF, THE ACFT HAD CLIMBED TO 200 FT MSL WHEN HE SUDDENLY REALIZED THE DENSITY OF THE FOG WAS THICKER THAN RPRTD OR ANTICIPATED. (THE ARPT ELEV WAS 81 FT.) HE SAID HE THEN EXPERIENCED VERTIGO (SPATIAL DISORIENTATION) & LOST CONTROL OF THE ACFT. SUBSEQUENTLY, THE ACFT HIT THE TOPS OF TREES & CRASHED IN THE PAWCATUCK RIVER. AS THE ACFT SANK, THE OCCUPANTS EGRESSED, THEN SWAM TO A DOCK WHERE THEY RCVD HELP.