NYC83FA128

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.