ON THE PREVIOUS DAY, THE PLT HAD FLOWN TO POUGHKEEPSIE, NY. BEFORE HE DEPARTED ON THE RETRUN TRIP, THE MANAGER OF A FLT SCHOOL INFORMED HIM THAT THE WX WAS BAD; HOWEVER, HE TOOK OFF AT ABOUT 0912 EDT. WHILE ENROUTE, THE ACFT COLLIDED WITH TREES NEAR THE TOP OF MOUNTAINOUS TERRAIN AT AN ELEVATION OF ABOUT 3400 FT. AFTER IMPACT WITH THE 1ST TREE, THE ACFT CONTINUED ABOUT 500 FT BEFORE IT CAME TO REST IN THE WOODED AREA. NO EVIDENCE OF A PREIMPACT, MECHANICAL FAILURE WAS FOUND. STATE POLICE OFFICERS FLYING IN A HELICOPTER REPORTED HEAVY RAIN & LOW CEILINGS IN THE AREA. ABOUT 34 MI NORTH-NORTHEAST AT ALBANY, NY, THE 0948 EDT WX WAS: ESTIMATED 1000 FT OVERCAST, 6 MI VISIBILITY WITH FOG, TEMP 55 DEG, DEW POINT 54 DEG, WIND 60 DEG AT 10 KTS, BREAKS IN OVERCAST WITH HIGHER CLOUDS VISIBLE. THE PLT PREVIOUSLY HAD A STUDENT CERTIFICATE, BUT IT HAD BEEN REVOKED BY THE FAA FOR VIOLATIONS.