Firstly, the option to mount a horse, mule or donkey to tame is very temperamental. Often the option simply does not exist and also cannot be fed.

If one is lucky enough to find one of these entities that will actually accept the rider, once tamed, the saddle item will not equip. Similar to attempting to equip the entity with a piece of cobblestone.

1. Approach entity with empty hand
2. Attempt a mount until tame
3. Open entities inventory
4. Select saddle