Waxing is important, especially the top. Do it however you can. As Jon said, two coats on the top are better than one, though he has a lot more sun especially since he doesn't cover his.
As for covered storage. I would cover in your case. Notice 'Jon in AZ' is probably from Arizona where they do not get the temperature extremes and humidity you will get in NY and as I do in Mass. I can fortunately keep my Scamp
in a barn for winter storage. But the barn is not tight and even then after a cold night turning to a warm humid or rainy day, every piece of metal, nut, bolt, screw, etc. becomes totally wet, though not as bad as being outside. I therefore put my Scamp
on jack stands under the axle
tube, remove the wheels and store them and put a large grocery bag over the brake drums with the handles tied tightly behind the brake backing plate. The brakes
always work in the spring and I am happy.