DURING AN IFR ARRIVAL, APRX 1 MI FROM THE OUTER MARKER (OM), THE PLT ASKED FOR A DESCENT FROM 3300 FT MSL & WAS CLEARED FOR THE LOCALIZER, RWY 1 APCH. THE PUBLISHED MIN ALT AT THE OM WAS 2100 FT. THE PLT REPORTED AT THE OM, AND 11 SECONDS LATER, THE CONTROLLER ASKED IF HE WANTED TO MAKE A 360 DEG TURN TO LOSE ALT. THE PLT DECLINED, BUT HE MADE 2 S-TURNS WHILE DESCENDING ON THE APCH. HE STATED THAT AT 800 FT MSL, HE APPLIED CRUISE POWER, CHECKED HIS TIME & NOTED HE HAD 30 SECONDS REMAINING TO GET TO THE MISSED APCH POINT. SHORTLY AFTER THAT, HE HEARD A 'LOUD BANG.' HE THEN MADE A MISSED APCH, DIVERTED TO BURLINGTON, VT & LANDED FROM AN ILS APCH. AFTER LANDING FOREIGN OBJECT DAMAGE WAS FOUND ON THE LEADINGEDGES OF THE WINGS, PROP SPINNER & LEFT HORIZONTAL STABILIZER. TREE FOLIAGE WAS ALSO FOUND ON THE ACFT. THE CONTROLLER STATED THE ARTS TARGET WENT TO A NON-BEACON STATUS AT THE APCH END OF THE RWY (AT 500 FT MSL). THE MDA WAS 720 FT MSL & THE MIN CEILING & VISIBILITY WERE 400 FT & 1 MI. APRX 4 MI SOUTHEAST, THE 0034 WX WAS 400 FT OBSCD, 7/8 MI VIS, FOG.