DURING ARRIVAL, THE FLT WAS ISSUED THE CURRENT PADUCAH ALTIMETER SETTING. THE PLT REQUESTED VECTORS FOR AN APCH TO RWY 18, BUT THE ARTCC CONTROLLER (CTLR) COULD NOT ACCOMMODATE THE REQUEST. THE PLT WAS CLRD FOR A VOR/DME-A APCH. MDA FOR THE APCH WAS 1080' MSL (600' AGL). AT 2108 CDT, THE FLT CHGD TO THE FBO FREQ. FBO PSNL OBSERVED THE ACFT FLY OVER THE ARPT & ADZD THAT IT WAS TOO LOW. ONE OF THE PLTS REPLIED THAT THEY WOULD BE 'STAYING UNDER THE CLOUDS.' THE PLTS HAD PLANNED TO LAND ON RWY 36, BUT RPRTD THEY LOST SIGHT OF THE RWY & WOULD CHANGE TO RWY 18. SUBSEQUENTLY, THE ACFT COLLIDED WITH A TREE ABOUT 1 MI NNE OF THE ARPT, WHILE ON A WESTERLY HDG (APRX PSN OF BASE LEG FOR A VFR PATTERN). THE ACFT CAME TO REST ABT 700' WEST OF THE TREE & WAS DESTROYED BY IMPACT & FIRE. NO PREIMPACT PART FAILURE/MALFUNCTION OF THE ACFT WAS FND. APRX 30 MI WEST AT PADUCAH, THE WX WAS IN PART: 200' SCATTERED, 900' OVC VIS 3 MI WITH RAIN & FOG, WND FM 360 DEG AT 7 KTS. THE ARPT MANAGER ESTIMATED THERE WAS A 200' CEILING AT THE ARPT.