Yes in New York State and even NYC "New York City" it's illegal to drive with snow on your car and you can be fined if caught with snow on your car because it creates a danger for other drivers.
The snow could fly off your car and onto the windshield of other cars and cause then to lose visibility and then that can result in a possibly deadly wreck.
Even if it were not illegal to drive with snow on your car in NY or any other place you should still clean the snow off your car for the safety of yourself, your family and others on the road.
While your car is warming up it doesn't take too long to remove the snow from the car before driving off.
I always remove all snow that I can from my vehicle while my engine is warming up.