I wrote an earlier blog entry on this topic. The short answer is that in New York City, the Traffic Violations Bureau will likely be open despite any major snow storm because it brings in lots of money from motorist fines.
If the storm is significant and they see a that major numbers of motorist don't show, they sometimes will mail you a new appointment for the hearing you missed. If they think it was not a major storm, they'll mail you a suspension warning stating you missed your hearing. Best thing is to check the dmv website link above and go to your hearing if you have one.
There is a big benefit in showing up to your hearing in a major snow storm because the absentee rate of the police officers is higher-- if you get lucky, your case will be dismissed because the officer didn't show up.
You can also simply reschedule your case if you have never done so before from the comfort of your home if you do it before midnight the night prior to your trial at the dmv website link below for rescheduling:
Drive safe and good luck!