A big storm will be heading towards the Great Lakes this weekend, which will send a cold front through Long Island. This will bring rain on Saturday into Saturday night, followed by cold and windy weather on Sunday. A secondary storm should form in New England, which will bring snow for northern New England. Lake effect snow will bring heavy snow accumulations to parts of upstate NY (see image below) from Saturday through Monday with the potential for up to 20 inches of snow. It's also possible that a third area of low pressure may form off the coast, which could bring light snow to Long Island Sunday night.
Looking ahead to Thanksgiving, it appears that another storm will be approaching which could bring rain to Long Island and snow for inland areas. However, It's much too early to know any specifics.
The following image from the GFS model shows projected snowfall amounts for the next 10 days:
Image from tropicaltidbits.com