It's at the Fort Wildernesss Campground, and you don't need any passes. You can just take the boat over from the Magic Kingdom. We like to break up our MK day by taking the boat over to FW for lunch at Trail's End and then we visit the petting farm and stables. It's a nice relaxing break! My little one LOVES it there.
There's also a petting are at the Animal Kingdom at Conservation Station. Of course, you have to use park passes to get into AK to get to that one.