A weak cold front will be approaching from the west today, and a low pressure system will form tonight and pass inside the 40/70 benchmark. This will be a mostly rain event for Long Island, although it should end as snow tomorrow morning into early afternoon. Most of today and tonight will just be cloudy. Rain should move in sometime after midnight tonight, and it should transition to snow sometime between 8 AM and 12:00 Noon tomorrow. The snow will then taper off from west to east between 1 PM and 4 PM. Suffolk should get a half inch or less, and Nassau may see up to 1 to 1.5 inches in far NW Nassau. Areas north and west of NYC should get 3 to 5 inches of snow.
The remainder of the week will then be dry with moderating temperatures into the mid 40's by the weekend. The next storm approaches the area on Monday, and since it will pass to our west, we will be on the warm side. This will bring rain to Long Island, and it should hold off until Monday night, although the timing could still change.
The following image is from the Euro, and it shows snowfall amounts through Thursday:
Image from eurowx.com