Yes they can deflate. They can pop, but it's not terribly loud. At least it's not an explosion. We've had one killed by a Boxer (teeth) and one killed by the Stallion (squished). We bought the least expensive ones we could find at Walmart, so if one is destroyed it's not the end of the world.
My friend has an equi spirit ball. We do not allow horses to play free with that one. It's only for controlled or monitored pushing around. The dogs are no longer allowed to play with them.
We were getting a larger-than-normal exercise ball from Walmart. We bought a bunch of them and I'm glad we did because I don't see them there any more. They are an ugly gray, but they are really very large.
I also have a five foot "cage ball". It's got a very tough outer nylon shell, but it's got a very delicate balloon like interior, so we only play with that one on rare occasions. It cost about $300 give or take. It's inflated, played with (we do mounted play it because the horses can't trip over it), then deflated (which is always good for gut wrenching giggles because of the cool squealing and farting sounds it can make while deflating) and stored away.
If you have a more aggressive player on your hands, the equi spirit might be a good choice if it's affordable, or if it's something you just want to leave in a paddock, then one of jolly balls with the handles might do the trick!