I live in New York. The last several winters we've been getting frequent heavy wet snow, and I store mine outside. If you have the digital, you may want to consider bringing the generator indoors.
After going through four covers; I gave up on the Bradley covers. They are very susceptible to UV damage, and in the summer my smoker gets a lot of direct sunlight. The sun causes the cover to become hard and brittle, and during the winter months it is prone to cracking. A couple of years ago I purchase a third party cover, and I'm very pleased with it. There are no signs of UV damage, and it still remains somewhat flexible during the winter; so it will not crack. Their is no problem with moisture, as it has an air vent. There are adjustable side straps to keep the cover secure.
ICover-Bradley 4 Rack Cover