NY Campgrounds W/Hookups open in winter?

There are not many campgrounds open during the winter, and I don't know that many offer water hookups during the winter. The spigots and hoses freeze, and if water freezes in them it can cause burst pipes and fittings and so forth. Electricity is more readily available because electric wires aren't affected by the cold weather.

The Campground Owner's of New York, a trade group that represents many commercial campgrounds, publishes a directory guidebook that lists the member campgrounds and their operating dates. It looks like there are maybe a dozen or so scattered around New York state that operate year round.

Never seen a trailer on skis... ;)

Unlikely you will find a park with water turned on - electricity, maybe... Try this link:
https://www.allstays.com/Campgrounds/New-York-am-all-year.htm