Animals on Shabbos
5. One is allowed to lead a horse [through the public domain on Shabbos] by a rope attached to its bridle, provided one holds the end of the rope so that less than a "tefach" (1) protrudes from one's hand (2). Similarly, the part of the rope that hangs between one's hand and the animal should not reach within a "tefach" of the ground (3). Thus, if the rope is very long, one should wind it around the horse's neck.
(1) Opinions among the authorities as to the exact length of a 'tefach' ('handbreadth') range between 8 and 10cm ( 3 to 4 inches).
(2) If a "tefach" or more is protruding from one's hand, it looks like one is carrying a separate piece of rope. This type of prohibition is called "Ma'aris Ayin," and forbids doing anything that others might construe as a transgression. According to the letter of the law, one only violates this rabbinical prohibition if two "tefachim" are protruding, however, the custom is to be stringent (Mishna Berura 305:50).
(3) If it would drop lower than a height of one "tefach" from the ground, it no longer looks like a rope with which one is leading and controlling the animal, but rather a burden (Mishna Berurah 305:51). According to others, the reason stated in note (2) applies here as well.