This may or may not be obvious, but there are different kinds of "winter" riding. In snow (even heavy falling unplowed snow) you need tires with some good tread. But on ice, no amount of tread is going to help. For that you need studs.
I have never ridden studded tires, so I can't say if you would want to be riding them all winter, but really, especially in NYC where the OP is, how often are the roads really icy? Around here (South Eastern Ma.) there has only been one day this winter when the roads were too icy for me to ride: during an ice storm. (Of course there was also that morning last month when I hit black ice and went down hard on my side. Twice. Hmmm....)
But I bet you won't encounter that very often. and if not, just get some good deep-treaded tires.