In New York City, March can vary. The beginning of the month is cold usually in the 40 s but by the end of the month average daytime highs are in the mid to upper 50 s. The daytime temperature in March usually ranges anywhere from 30 to 75 degrees. It could snow but nothing really major. But the temperature varies greatly in different parts of the city. In March when the ocean temperature is still very cool, the temperature in Manhatten can be as much as 20 degrees warmer than on the coast like Coney Island or Kennedy Airport.
It depends on what part of New York you are talking about. Upstate from Buffalo to Albany to the Adirondacks it will be cold and wet and snowy. Downstate around the city, it will be cold and wet.
It can be sunny at times, snowing at times, and raining at times. But it s going to be cold so be prepared. Good luck!