Dogs and other pets are not allowed in the Cactus Garden. This is for their safety. The cacti are exposed and close to the path. There's a very high risk that animals will come in contact with cacti if they stray from the path at all.
Under The Americans with Disabilities Act (ADA), service animals (dogs and miniature horses) are permitted and must be harnessed, leashed, or tethered, unless the individual’s disability prevents using these devices or these devices interfere with the service animal’s safe, effective performance of tasks. In that case, the individual must maintain control of the animal through voice, signal, or other effective controls.