I'll never get used to ice. I have the coordination/balance of an elephant on rollerskates!
I've lived in the midwest for over eleven years - I'm aware of what I'm "supposed" to do when it snows. And, just as it happens here, I'm sure some people in New York don't get a chance to clear their walkways the second the first snow hits the ground. Much like New York, snow doesn't need to be cleared immediately here. There is plenty of time for ice to build up (i.e. while someone is at work or sleeping) before one has to worry about a fine.
Icy sidewalks happen everywhere, even New York.
Yes, there are icy patches here and there, but there usually aren't entire streets (or networks of streets) that are covered with ice from one end to other.
Today, I had to walk to my doctors' surgery and had to walk on ice the entire way. Now admittedly, the surgery is pretty close to my house, but if any place should have a clear path in front of it, I'd think it would be a surgery.
In New York City, people shovel as soon as they can, whatever time of day that is.
Yes, the law doesn't say that you have to shovel snow as soon as it starts to fall - but people do it because they know that it's easier to shovel snow when it's fresh than after it's accumulated and turned to ice.
My ex used to work for the New York City Department of Sidewalks (part of the Department of Transportation), the department that fines people who don't shovel their walks.