Questions about being a "street" vendor

I put street in quotations because I'm not sure if that's what I'd qualify as.

I make and sell homemade dog treats with various naturally-colored icings, all beneficial for dogs. I wanted to do an "ice your own dog treat" stand at the very dog-friendly farmers market, but after speaking with the director this afternoon I'm leaning away from that. They require both Saturday and Sunday for the entire summer. Having another FT job and being my only employee, this would kill my summer, for probably not enough payoff.

I was thinking about doing the same thing, but instead setting up at large dog parks in the area. How would I go about figuring out 1) if this is legal 2) how to obtain proper permits/licenses 3) anything else I'm not thinking about.

Thank you very much r/smallbusiness! The advice on this sub is amazing.