Animals on Shabbos
2. A horse may go out [into the public domain on Shabbos] wearing a harness or a bridle, but not wearing them both (1). It is permitted to wind the straps of the harness around its neck; they must, however, be loose enough to enable placing one's hands between the straps and the animal's neck to lead it if it tries to pull away (2). One may move the harness and place it on the animal as long as one does not lean on it, since it is forbidden to lean on an animal on Shabbos (3).
An iron bridle may not be placed on a donkey, for this is considered an extra safeguard. A cow or an ox that does not require guarding, may not be allowed out into the public domain with a rope around its neck, unless it frequently runs away. A rope tied to a horse's mouth is considered to be a burden, because it is not an adequate safeguard, since it slips from its mouth. It is not comparable to a harness that is attached to its [entire] head.
(1) As we saw in HY 87:1, anything which is unnecessary for control of the animal is considered a burden, and is thus prohibited on Shabbos. Either a harness or a bridle alone is sufficient for control of the horse.
(2) Rashi and the Ran disagree, allowing even tight wrapping if that is the ordinary mode for wearing these straps.
(3) 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).