Will RV parks have a problem with this toyhauler?

Interesting question.

My short answer is not a problem.

I think almost every park would be concerned about the condition of your RV, not its construction. You might find the rare park where the owner or manager is so short sided they can't think beyond a conventionally constructed RV. You might get the legitimate question about your having horses with you, however. Once that issue is solved, I think a problem would be rare.