Regarding freezing drizzle for Long Island and the Tri-state area from the National Weather Service:

As we get closer to Monday morning this results in a profile that supports drizzle, as there will likely be no ice nucleation. With surface temperatures below freezing, this will result in a period of potential freezing drizzle in the early morning. Confidence is low in coverage and intensity and have decided to hold off on a Winter Weather Advisory. This will have to be monitored by subsequent shifts and an Advisory or SPS may be needed if ice accretion looks more likely. It is possible that untreated surfaces become slippery and impact the morning commute. There is a slight chance to chance of freezing drizzle across the whole area for just a few hours after daybreak on Monday morning. Higher chances are across southern areas. This quickly turns into plain rain in the NYC metro, Long Island and the coast as temperatures rise above freezing. These southern locations will then likely only see plain drizzle or plain rain for the rest of the day. Accumulations of liquid rain are only expected to be a few hundredths of an inch. By the afternoon as the column saturates a bit more there can be a switch over to more steady rain instead of a drizzle. Being in the left exit region of an approaching jet streak will likely help this intensity of rain increase.

The following video is from 4 AM tomorrow to 4 AM Tuesday from the NAM: