I drove a G35 Coupe last winter around NJ/NY/CT with Yokohama Advans (with plenty of tread left) until the first dusting hit. I was nearly unable to get out of a mostly FLAT driveway with about 0.25" of snow in 25 F temps. These problems would be exacerbated by the M3's wider tires. So, I would say that in NY you really should get winter tires.
Max performance summer tires like the Advan, PS2, RE050A/01R, PZero, etc are very very dangerous in the winter, if only because of the low temperatures. They have poor grip even in the dry, they become very hard at sub 40 F temps. I cannot tell you how bad they are when the roads were not perfectly dry, I would not even risk it at all. I had traction control coming on at 5 mph coming to a stop on anything that wasn't completely down to the pavement. My brother actually had it even worse with his 335i because of the slightly wider tires + lack of an LSD, had to be pushed up a hill and out of a friend's driveway after a tiny amount of snowfall.
I bought cheap wheels and winter tires from Tire Rack. I did my research and ended up with Michelin Pilot Alpin PA3, which were new for last year and BMW's recommended winter tire IIRC for the M3.
The dry handling of this tire is incredible for a winter tire... I'm fairly sure it is better than any all season out there. I felt that in the dry, this tire was almost at the level of a summer tire (in the summer!) when the temperatures stayed below 45 F. Bottom line, in near freezing temps, a winter tire will probably have more grip, even in the dry, than a summer tire.
The snow performance was decent, it probably isn't up to the level of the agressive WS60 Blizzak, but I got up a steep hill with about 2-3 inches of snow on it, and I felt very confident with it. I would go as far to say that I would feel more comfortable in a RWD vehicle with winter tires than a FWD car with all season tires. Downsize if you can, just make sure you keep your diameters within 3%. I ran the smallest wheels that would clear the brakes (17", to make tires/wheels cheaper) and 225's all around with staggered profile. Wider tires are not your friend in the rain or snow.
This year I'll be driving a Z4M Roadster in the winter
, so we'll see how that works out. I'm sure it will be fine with snow tires, the ground clearance will be the biggest problem.