We now have designated Off-Leash Wilderness Trails in the North-East section of the park. So long as your dog can be trusted to not harass people, wildlife or other dogs, they can frolic freely in the forest. The off-leash section is marked in pink on the map below.
Note: this does not include the main Zoo Trail. Dogs must still be leashed on the Zoo Trail and throughout the rest of the park, where an off-leash dog is a fineable offense.