Check out the right to farm rules for NY. For instance, in NJ I have right to farm as long as I have 5 acres. That might be a start. Also, I would think they should have notified you if they were rezoning your property. So, if you had been ag and over the acreage for RTF, then you should be able to get them to rezone you back to ag. I would think that you would be due a variance at minimum. That said, many urban areas allow a few hens, so you might be fine regardless. Check your townships ordinance.
As to the winter issue. I do nothing special besides an extra bag of bedding on the floor. The biggest problem with cold is condensation and drafts. Condensation causes a rapid loss of body temp and bad frostbite, drafts will cause rapid hypothermia. If they can stay dry and out of a draft they will be ok. I have no heat and about 6 square feet of open ventilation all winter long. The openings are at the very top of the coop in the eaves. It allows for ventilation of moist air, but without a draft. I have seen coop designs for the wintery midwest that are long and completely open (fencing only) on one of the short ends. I think they place the open end parallel to the prevailing wind so they have massive ventilation, but no draft when they are roosting in the far end of the coop. This past winter, you all know how bad it was, I had only minor problems with frostbite combs on my leghorns and legbars (huuuuuuuge combs and wattles). It was only because the knuckleheads practically dipped their heads into the waterers and I couldn't get them dry enough (they are skittish to begin with, let alone when a human with papertowels comes at them to get them dry). I didn't even use vaseline or anything. I have one rooster in an open air tractor that has a "box" on one end. He sleeps in the corner away from the door. Not a bit of frostbite. In fact, he was one of the best looking when spring came around.
Use of lights, insulation (which they will eat if they can), heatlamps, etc, is a detriment in my opinion. It is expensive and causes them to get used to a warmer coop and then they get really cold when they go out. Keep them dry and out of the draft when they roost. They will be fine. If they get wet (like from wet snow) bring them in and dry them off. Wet feathers do not insulate at all. I think certain breeds might need supplemental heat (seramas, silkies, etc), but then again, I have friends with all of them and they do not use heat.
One variable that you may not have though... I have 40 chickens in the big coop (10 foot ceilings, 100 square). They make a LOT of heat, and humidity. If your coop is the right size for the number of birds and is well ventilated you will be fine though. My bantams are in a low ceiling coop, it is only 4 feet high. I close a lot of the vents in the winter, but they do ok.