My Personal Weatherman™
Analysis from the new NAM run:
The NAM is showing heavy snow for Long Island between around 8 AM and 2 PM with additional accumulations of around 9 inches just in that 6-hour period. However, after that it starts to show the rain advancing in from the east. So, it's possible that most of the accumulating snow will be done by late afternoon in central to eastern Suffolk. You can see in the video below that it even shows it changing to rain in western Nassau tomorrow night for a while before going back to snow. It also has more generally light to moderate snow for Tuesday into Tuesday night.
This video goes from 1 AM tonight to 7 AM Wednesday: