The rain should end by mid-afternoon today on Long Island, and then it should be dry and mild for the first half of the week with highs in the 50's and lows in the 30's. However, an approaching storm will bring an extended period of rain and wind to Long Island from Thursday late afternoon into early Saturday morning. Rainfall amounts of 1 to 2 inches with wind gusts as high as 40 mph are possible. The Euro has the heaviest rain around southern NJ with amounts over 2 inches just on Friday (see image below).
Looking ahead to the following week, it does appear that snow is possible for Long Island, but it's too early to know any details. The GFS is hinting at potential storms for March 7th/8th and 10th/11th that bear watching.
The following image from the Euro shows projected rainfall totals just for Friday, March 2nd:
Image from eurowx.com