A ram can be tied with a piece of skin on it’s male member in order that it should not be with a female. The female can go out with it tail tied up to make it easier for the male.

Chapter 305 Section 7

A donkey can go out with a saddle to keep it warm if it was put on before Shabbos to show it is needed.

Chapter 305 Section 8

You cannot tie the saddle tightly on Shabbos as you if will be using the animal.