Also, just for your information, once you get further north into NY state, particularly the closer you get to Syracuse, you in in the region famous for "lake effect" snows - dense snow squalls fueled by the warmer water of Lake Ontario (and to a lesser extent Lake Erie). I've driven this exact route in the winter, and one minute it can be sunny and then a few miles down the road you are in the middle of a snowstorm.
Not trying to be Mr. Doom and Gloom, but it is a phenomenon you should be aware of before setting out. These squalls are usually more intense early in the winter (i.e. December) before the lake begins to freeze.