Bambam where yoube from, I would be more worried about the salt air.
Yes covered is good and bad.
Good in that it keeps the weather off and bad as critters and moisture will do some naughty things unless you have a tent set up so the air can get in and out..
If you have the room, one of those 300 dollar car ports would work well, out of the sun and weather but still let air in and out. To be honest and I dont know what you have, letting it set out uncovered wont do to much harm as long as you make sure things are greased and chips have a coat of paint and the tires are filled though it also depends how often you use it.
Tires will over a period of time for lack of a better word, dry rot, get hard and just come apart on you.
SO you need to keep an eye on them covered or not.
Just take care of it, and covered or not, it will serve you well