87:8 If a person has a non-Jewish employee who rides the Jewish employer's animal on Shabbos, he need not prevent him from taking the animal out for water. This is because the prohibition against riding an animal on Shabbos has nothing to do with the animal carrying a burden; under Biblical law, a living being is considered carrying itself and the rabbinic enactment prohibiting this was not applied to animals. Rather, the prohibition against riding applies the rider, so a Jew is not permitted to ride on Shabbos but this does not prohibit a non-Jew. Even if the non-Jewish employee places a saddle or a blanket on the animal to ride it, those are still considered subordinate to the rider. He should not, however, place any other objects on the animal.
87:9 One may direct a non-Jew to milk animals on Shabbos because of the distress it causes the animals ("tzaar baalei chaim") to go without being milked. The milk, however, may not be drunk on the same day, nor may it be moved (by the Jew, because it's muktzeh). Instead, the non-Jew should put the milk in a safe place. Similarly, one may direct a non-Jew to force feed geese once on Shabbos, because of unnecessary suffering to animals. (This refers to geese that have become accustomed to being force fed and can no longer feed themselves - MB 305:71. Nowadays, force feeding animals is considered cruel; this halacha is not meant to address whether or not force feeding is permissible, it merely reflects the reality that, historically, such things have been done.)