Just a warning about using treated posts or wood of any kind around animals. We recently had a mare get a puncture wound on her neck. No sign of ANYTHING being in it, but it simply would NOT heal. Couple visits to the vet, lanced it, drained it, kept it clean, etc...no healing. She rubbed against something and all of a sudden, neck heals up, shoulder opens up a wound. This time we actually sedated her and cut it wide open....found a 6inch piece of treated wood. As soon as it was removed, she healed within days. This piece of wood came from a trainers round pen and he'd never had an issue with it before.
Also, being from NW Kansas, we have never cemented posts. And most of our corner posts are not even braced. IF you can tamp properly (my hubby can't LOL) you should be able to get your posts solid enough to not need anything. We do use way bigger posts (12' or better) for corners so that does make a difference.