Cardinals,
I live in Eastern Washington and it gets pretty cold as it does in New York. I bring my batteries into the basement each fall. I store my trailer about 14 miles away.
I check them when I bring them in. This year they were at 12.8 volts. I do not ignore them until May. I will check them something like every other month. Usually I will have to hook them up to a trickle charge when they are down a bit. I will check the water level once or twice each winter. As spring gets close, I will make sure the water level is up and then charge them up.
I don't think it is a good idea to ignore these the entire winter.