Couple of thoughts that haven't been covered.
First, if there are leash laws in the jurisdiction where you are playing, and the park is public, keep your dog on a leash for the sake of all of us. I've been playing disc golf for 16 years, much longer than most. There is a lot of time and effort that goes into getting a course established on public property. Unfortunately, many folks in the communities may not like disc golf and are looking for any reason to bring it before a city/county commission to have it removed. I'm serious when I say that allowing your dog to go without a leash, despite whether or not you think it is a "well behaved" dog, jeopardizes the course. That's just a fact. I can assure you that public courses have been pulled for much less than dog bites, and those of us who've been around for a while understand. If the course is on private land and the owner is cool with a dog, by all means. But in a public park, they need to be on a leash or at home.
Secondly, I am an insurance executive by trade. Currently, the largest claim my company is facing involves a vicious dog attack. There are about 15-20 breeds of dogs that are excluded from most homeowners insurance policies. An HO policy does cover your liability stemming from activities outside of your premises. This was one of the excluded types of dogs, however, the underwriter allowed the dog because it was a professionally-trained service dog. The owner took the dog to a park and sat down on a bench to read. A child, age 6, was walking her small dog, which was on a leash. The parents were only a few feet away, and they assumed a service dog was obedient. The service dog bit the small dog, killing it instantly, and in it's fervor curled the child into the fray as the leash was wrapped around the child's wrist. The service dog then continued to maul the child until the parents were able to wrestle the service dog off. The resulting damage was nearly 7 million dollars in medical bills and plastic surgery. The child did survive. The owner was an old rich guy with a huge Umbrella policy so he had enough insurance that the company is covering the entire claim. All that to say, dog attacks are a huge issue. Most people think they have coverage for their animals, but if you have a Pit bull, Rottweiler, Akita, German Shepherd, unless you have a specific endorsement on your policy, you don't have coverage in the event of that liability loss. And if you're a renter, I can guarantee you don't have enough liability coverage for any dog attack regardless of what type of dog. Bottom line, anytime you let the dog off the leash, you could be setting yourself up for HUGE financial ruin. On top of that, you could be sued for negligence and hit with punitive damages as well. It's not worth it, and I see these claims daily. Be smart.