You must register your snowmobile if you operate the snowmobile in New York State. A registration is not required if the snowmobile is operated on the private property of the owner or private property the owner has a contractual right to use. A snowmobile that is registered in another state and owned by a resident of that state, but is operated in NYS, must get a NYS registration. New York State also requires a registration on trailers.
Visit the NYS DMV web site for more information.