Today and tomorrow will be sunny and seasonably cold on Long Island with highs in the 30's. Temperatures will warm up to 50 degrees on Saturday with increasing clouds in the afternoon. Sunday will bring rain with temps in the upper 40's as a cold front moves through. After the front passes, a wave of low pressure will develop on the front and head northeastward. The key will be how close to the coast does it come. At this time, both the GFS and Euro are bringing it close enough to bring some snow to Long Island sometime in the Tuesday or Tuesday night. The GFS is showing a few inches for Suffolk, and the Euro is showing amounts up to 6 inches (see image below). It's too early to tell the details, but it bears watching. After that, a second frontal system will approach for next Friday, which has the potential to bring rain changing to snow. There is then more snow potential the following week.
The following image is from the Euro, and it shows projected snowfall totals through next Wednesday: