Is a dog park a trail? Why would you care?
If you're walking your dog in a dog park, slip and fall and get injured, you're going to care. Especially if you want to sue the city that maintains the dog park. You should first understand that cities and counties have immunities for injuries that occur on trails because you're supposed to understand that there's an inherent risk in using the trail, and you're more likely to slip and fall there than on a city sidewalk, where it's more likely the city or county may be liable.
For Anni Amberger-Warren, she found out the hard way that she couldn't sue the City of Piedmont. The court of appeals ruled that the dog park (at least the off-leash section) looked more like a trail than a city sidewalk, and denied recovery for Ms. Amberger-Warren's injuries.
So, if you're out there walking your dog, be careful. It's a jungle.