I haven't run into much barking, but people 'walking' their dogs off-leash, or sending the dog out with a human too small to control the leashed dog, are frequently a problem.
My cat uses his discretion. The first few days in a park, he only wants to go out after dark, after the dogs are all in for the night.
After he learns the habits of the various dogs and owners, he starts going out in between walkies times. If we stay long enough in one park, he starts staying out all day, just hopping into the rig when particular dogs come out.
I don't ever leave him outside without me.
Some parks, in the evening, cat and I take turns getting up every 5 minutes to see if the off leash pitbulls have been taken inside yet, so he can go out.
What kitty really likes is boondocking! No dogs, and a lot of rodents :B.