Mounts (horses, donkeys and camels) are somewhat protected on your own land. But not entirely.
Mounts on your own land can not be ridden by other players. However, it is possible for a player to remove your saddle and/or saddle bags. This is an API limitation. 😔
In order to protect your mount you need to either pen your animals in and remove their saddle and saddle bags (as shown above). The other way is to build a stable for them and then use lockable doors to prevent other players entering the structure.
P.s. You can also buy mounts at any time using the /buy command. Just make sure you have the correct saddle ready in your inventory!