87:6 If two or more animals are tied together, one may not hold the bridle of one in his hand and draw the rest along after it, even in a city that has an eiruv (because it looks as if he's taking the animals out to sell them in the market. Therefore, it makes no difference if the animals were tied together before Shabbos - Mishnah Brurah 305:49). However, one may hold the reins of several animals in his hand and lead them all together so long as he holds the ropes as described in 87:5.
87:7 Chickens may not go out with strings tied to them as a form of identification or to keep them from breaking things. One may, however, tie their feet to keep them from running away. Similarly, two legs of horses grazing in the field may be tied together to keep them from running away so long as they aren't fettered or hogtied. Fettering entails tying one of the horse's forelegs to one of its hind legs; hogtying involves tying one of the animal's hind legs upwards so that it can only walk on three legs. These are forbidden even during the week, because doing so constitutes causing an animal unnecessary pain.