Animals on Shabbos
3. A saddlecloth should not be worn [out into the public domain on Shabbos] by a horse or any other animal, with the exception of a donkey, because donkeys have the tendency to become cold (even during the summer), and therefore, it is considered its garment (and not a burden) (1). If it was tied onto the donkey before Shabbos, it may wear it out into the public domain on Shabbos; however, if it is not tied to it, one is forbidden to allow the donkey to walk out wearing it on Shabbos, because [the Sages were concerned] that it may fall off, and the owner will end up carrying it through the public domain. One may not tie the saddlecloth onto the donkey on Shabbos (even using a permissible knot), because one would have to come close and lean on it in order to do so (2). One may, however, on Shabbos, place a saddlecloth on the donkey in a courtyard because of the cold, provided it does not walk into the public domain.
It is forbidden to place a saddlecloth on a horse at all unless it is so cold that the horse might be affected. Similarly, during the summer, when there are many flies that cause it discomfort, a saddlecloth may be place on the horse, provided one is careful not to lean on it in the process.
It is forbidden to remove a saddlecloth from either a horse or a donkey on Shabbos, because leaving it on causes no discomfort to the animal (3).
(1) As we saw in HY 87:1, anything which is unnecessary for either the control or the well-being of the animal is considered a burden, and it is forbidden for the animal to walk out into the public domain with it on Shabbos.
(2) There is a rabbinical prohibition against riding or even making use of
an animal's body on Shabbos or Yom Tov (Beizta 19a). The reason given by
the Talmud Bavli is a concern that one may break off a tree branch (a
biblical violation of Shabbos) in order to strike it while leading it along
or riding it. According to the Jerusalem Talmud, the reason for the
rabbinical prohibition is a concern that one may come to lead the animal
into a public domain with a load on its back, which we saw is Biblically
prohibited (Aruch Hashulchan 305:16).
(3) Any unnecessary strenuous or bothersome activity ("Tircha Shelo LeTzorech") is rabbinically prohibited on Shabbos.