In multiple worlds, I have had horses despawn. In this specific world, I have/had 2 horses and a mule. One of my horses was named along with the mule and still despawned. Luckily, I took off the saddle after each use due to encountering this bug more than once. However, unfortunately my best horse that despawn was wearing horse armor, and it disappeared along with the horse. The only thing that stays is the lead the horse was attached to.

In the attachment below, there are 2 leads on the fence. One without anything attach, and the other is attach to my horse I got a couple of (Minecraft) days ago. It will eventually despawn after a period of time too.