If you really want to play in decent conditions, I would try South and West of NYC in New Jersey where courses are sandy and in the Pine Barrens. Basically Pine Valley was set up for this shoulder season, but realizing that may not be an option, I would try Pine Barrens (closest to NYC), Pine Hill, Blue Heron Pines, Twisted Dune and Atlantic City (which has alot of wind chill exposure). Forsgate too which is private, but may accept a call at that time of year.
On Long Island, you will lose a week or two of growing season, but Tall Grass and Long Island National should be open.