For right now, we can break down Wednesday's situation as follows for right now with much more details known by Monday...
There WILL be a strong coastal storm but the path is still VERY UNCERTAIN. The air WILL be cold enough that any precipitation in the New York City area will be snow. Just one of the things that will affect the track are when the axis of the trough becomes negatively tilted, which in turn affects when/where the low pressure system will makes its backtrack as it turns north to bring snow.
It's also good to remember that even though it is officially Spring by all definitions (Astronomical & Meteorological), mother nature doesn't always care. Snow in late-March is not uncommon. After this coastal low, the atmosphere does begin to take a greater Spring-like turn.
Enjoy the weekend!