DRG AN IFR ARRIVAL, THE ACFT WAS VECTORED FOR AN NDB RWY 23 APCH TO THE WESTMORELAND COUNTY ARPT. AT THE NDB FINAL APCH FIX (8.1 MI FROM THE RWY), THE CREW TURNED INBOUND & CONTD TO THE ARPT. THEY CONTACTED THE TOWER & REPORTED OVER THE ILS OUTER MARKER (AN INTERMEDIATE POINT ON THE NDB FINAL APCH, 3.9 MI FROM THE RWY). THE TOWER ISSUED THE LOCAL LANDING ADVISORIES & CLEARED THE ACFT TO LAND. MOMENTS AFTER THE COPLT ADVISED THE CAPT THAT THEY WERE 15 SEC FROM THE MISSED APCH PT, THE ACFT COLLIDED WITH TREES. IMPACT OCCURRED 3.8 MI SE OF THE ARPT AT THE MIN DSCNT ALT (MDA) OF 1900 FT MSL. AN EXAM OF THE ACFT RECORDS INDICATED A RECURRING & CURRENT SQUAWK CONCERNING THE HSI SLAVING SYS. JUST BEFORE BEGINNINGTHE APCH, THE LATROBE WIND HAD CHANGED FROM 230 DEG AT 4 KTS (A HEADWIND) TO A STRONG QUARTERING TAIL WIND. DRG ARRIVAL THE CREW WERE ADVISED THE WIND WAS FROM 340 DEG AT 18 KTS. THEY HAD FIGURED THEIR TIMING TO THE MISSED APCH PT BY USING A GND SPEED OF 120 KTS. EARLIER THAT DAY, THE SAME CREW & ACFT HAD TERMINATED THE SAME NDB APCH, 1 MI EAST OF THE ARPT.