Riding 23's the other day in the slush felt pretty sloppy / unstable to me. I also had to be really careful and slow with taking corners.

Riding a mountain bike with knobbies last year in Portland when it dumped felt pretty damn stable and natural.

If I lived in an area that had snow on the ground for a constant three months or so, I'd say a fixed mountain bike w/ knobbies or studs would be the ultimate work horse / utility bike. Lots of fun for sure.

Wider makes a lot of sense when the snow melts a bit and then freezes into quasi-ice. If you always ride on fresh snow (possible, in metropolis like Montreal where they clean the snow very quickly), or you are blessed with a climate where, once it gets below freezing it doesn't get back until spring, you won't aprecciate wider tyres, and I will agree with you that thinner makes more sense. But I have never had those condition for more than 2 days tops.

"Annealed snow" as I call it, is a bytch.

Also: ice.

I have one of these on the front:
https://www.mec.ca/Products/product_d...=1201792777365
Regular knobbie on the back.

It may look like overkill, but that tire kicks ass.

I woke up this morning to 15 mm of frozen rain, i could barely stand up in my driveway. People at the bus stops where holding on to poles and stuff.
I rode 9 km to work no problem.

Forecast for tonight says 5 inches of snow.

I'm running Ritchey cross tires on my bike and they are just wide and knobby enough to help me get through snow and ice in Indiana, but no overly cumbersome to seem awkward on clean roads. It is kind of a compromise on both sides but as of now they are the best of both worlds.

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.