I'm not sure code enforcement could do much about the hoophouse style, they don't have a foundation so it's just sort of a lawn ornament. Probably depends on the exact wording of the code, and how much you care about bothering the neighbors.
I don't think I like this "new America" that we live in. I'm glad I live in the country and can largely do as I please.
Oh, they do research on the professional version of the hoophouses on campus here. They have held up under the snow load of Michigan's upper peninsula, and can maintain cold season crops over winter here. The fancy versions are about $20,000 for 18x100', they are automated to roll up the sides if they start to overheat. Of course I want one!
I don't think the trailer would work, if you are trying to do season extension. They need to be connected to the ground to store the heat during the day.