Storms could be an issue - storm won't usually sink a houseboat or destroy a RV trailer.
But it might very well smash a residential airship into the ground even if securely moored just due to the sheer size of its gas envelope being effectively a giant sail.
A residential-class airship would probably be limited to visual flight rules conditions and have to land or at least be docked every night. You'll want to do that for a variety of comfort reasons, too -- water is heavy, so finding a campground with electrical and water hookups would be preferred.