86:7 Water that one would not normally wash in, but which would be reserved for medical use, may not be used to wash in on Shabbos, as it will appear that it's being done for medical reasons. This applies when one remains in the water; if he doesn't stay in the water, it is permitted because he is clearly just cooling off. Regarding natural hot springs where one bathes only for medical purposes, it is forbidden to bathe in them on Shabbos for medical purposes, even if he does not remain in the water. (Mishnah Brurah 328:137 permits one to bathe in hot springs for a brief span of time.)
87:1 The Torah tells us (Exodus 23:12), "your donkey and your ox will rest," from which we see that animals belonging to a Jew must also rest on Shabbos. Therefore, one may not permit his animal to transport any kind of a load, even if it went out on its own accord. If one's animal carries a burden to the public domain, the owner has violated this commandment. Even something placed on the animal as an ornament is considered a burden, though something intended to heal it, like a bandage placed on a wound, is permitted. Similarly, anything that is necessary for guarding the animal is like clothing is to a person, and therefore permitted. Something that is for added security is redundant and forbidden. Something that doesn't protect this particular animal, even though it would serve as protection for another animal, is considered a burden and prohibited.