After dying while riding a horse a large enough distance away from your respawn point, the horse will disappear after reloading the world if it wasn't loaded after you respawned.
To reproduce
Set your spawn somewhere
Teleport ~1000 blocks away
Summon a horse
/summon horse ~ ~ ~ {Tame:1b}
Ride the horse
Summon a zombified piglin (or another mob)
Let it kill you
When back at your respawn point, reload the world
Teleport back
→ ❌ The horse disappears
Video
[media]Original description
I was riding my horse when I was killed by an enderman. I was heading back to where I died and for some reason I was somehow teleported onto my horse. The game glitched me onto the horse. After I was glitched onto the horse, no sounds could be made. The horse couldn't make sound, but other animals were still able to move but couldn't make sound. Chunks were still rendering though. I was looking at a map when the game glitched. When I was on the glitched horse, the map thought I was in the same position as I was before the game glitched. When I reloaded my world, I was in the same area as the horse, but the horse was gone. I tried using commands to find the horse, but it couldn't find it. PLEASE FIX THIS
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Comments

I'm unable to reproduce that desync issue, but it seems like there's indeed an issue with the horse disappearing after death.
Doesn't seem to happen in 1.16.5.

can confirm

Confirmed for 21w06a.