I play on Single player as well as a LAN world with my husband and I have had problems with animals disappearing when I (or we) log out.

I farm all types of animals and multiple different ones have just disappeared. With horses, donkeys, and mules (so far, only tamed) they have disappeared after logging out and back in. They have been ridden, tied, and free roaming. This has happened more with horses than any other animal.