Watertown (ART) is in the middle of nowhere. Be prepared to cab it or rent a car. If you are lucky, you might get a hotel room if you book ahead of time, although be prepared not to if something is going on at Fort Drum. When Ft Drum gets an influx of soldiers and their housing isn't available...guess what??? They stay in hotels. The mall sucks. Sackets Harbor and Alexandria Bay are both nice, but again, you need to have vehicle transportation. Nothing is in walking distance from Arsenal Street motels and there are not sidewalks, so pedestrians beware.
I can't imagine why anyone would want to waste time flying into this place unless you had a good reason to.
And, yes, if you are going to Watertown during winter months, you will freeze your butt off and more than likely your flight will be delayed/cancelled.