The barn I ride at just had to get rid of a new pony because he turned out to be a chronic strangles carrier.
This happens when the bacteria gets into the guttural pouch, from which it is nearly impossible to extract using antibiotics. You and I don't have guttural pouches - they are found in equines, rhinoceri and tapirs, as well as in some bats, hyraxes and one species of mouse. They connect the middle air to the pharynx. So, they're kind of part of the inner air.
The purpose of the guttural pouch is to cool the brain during extreme exercise - a useful adaptation for a being that relies on running for defense. But when it becomes infected, it can be very hard to treat.