I live on eight acres in the rural SE Arizona desert. We have prickly pear, four different cholla and saguaro on our place. The worst of all are the "teddy bear" and "jumping" cholla.

I have had four dogs since we moved here and I'll pretty much endorse what skcreidk said; dogs eventually learn to avoid the stuff. This appears to be more than can be said for some humans.

Dog breed does enter into the equation a bit. Our Malamutes both learned quickly to avoid the stuff. Our golden retriever took a bit longer to learn but she was young. Our West Highland terrier never seemed to really figure it out.

I always have a comb with me when I'm out with the dog (our golden is the only one now). She will generally stop and wait for me when she picks up a thorn cluster. She is less likely to try to bite one out of her paw now but still tries it on occasion. I have spent an hour trying to get the 1" long, barbed cholla spines out of her tongue, gums and the roof of her mouth. The spines soften after they have been in place for a while. Sometimes it's best to just wait for them to get a bit infected and they will slide out easily.

This is a problem that must be managed, you won't be able to solve it.