We have recently discovered two spots not far from our AZ home where we feel we can 'safely' run our dogs off leash. (These locations will remain unidentified to protect the innocent - and the guilty!) There are still dangers of cactus but fortunately our dogs are well trained and if they get close to cactus or too far away, we call or whistle and they return right away - well, 99% of the time! I always carry pliers to extract thorns from their paws, just in case.
I was told by a local veterinarian that snakes do make appearances in every month of the year here so we are still on the lookout. Most snake bites occur to dogs that run off leash so this is still a big worry. I must read up more on snake habitats so I have a better idea where they may hang out. The two spots we run the dogs are like construction sites - where the land has been cleared of most vegetation. Not too interesting to look at but that means no cacti and very few plants in these areas.