What's in a good all purpose city commuting winter tire? How do I determine what factors lead to a good all purpose city commuting winter tire? Does the rim matter?

I'd like to not have to worry too much about looking out for and avoiding black ice, mainly because I'm not sure you can even do that reliably?

I'll be riding on roads and bike paths but if I encounter an unplowed section, I'd want to be able to get thru the snow without too much trouble.

I am interested in NYC so please factor that into your reply if possible, although a general answer would be great. FYI in NYC in January there's 8 inches of snow across 4 days, and 4 inches of rain across 10 days. Average temperature is 26F low, 38F high.
Your best bet for all around tire in the winter is going to be a cyclocross tire. They are made to race in grass, snow, on pavement, in sand, singletrack, and just about any way possible. They also have different types of treads for different conditions. You can't beat the Hutchinson Bulldogs, if you are looking for something more affordable, maybe the Maxxis Locust CX. CX tires offer low rolling resistance in the center of the tire, and have good grip on the sides. A less aggressive tread would be found on something like the Kenda Happy Medium. Give those a shot this winter and you shouldn't be disappointed.