The prohibition against causing animals to work on Shabbat includes not only actively drawing the animal along as it performs a prohibited labor, but also merely causing it to perform the prohibited action; for example, if the animal has a load on its back and one calls to it, thereby causing it to carry outside a permitted area.

One may not cause an animal to perform work on Shabbat, but one may whistle or signal to an animal to come to him.

It is prohibited to ride an animal on Shabbat, regardless of whether it belongs to the rider or not, and regardless of whether there is an eiruv.

A blind person who requires a guide dog may walk outdoors with it.

Further reading: For the story of a cow that kept Shabbat, see A Concise Guide to the Sages, p. 280.