Ridden entities disappear on relogin

Horses, Minecarts, Boats disappear after relogging.

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Steps to reproduce:

1. Play a single player world
2. Ride a horse (with a saddle?)
3. Click ESC then open to LAN
4. Save and quit to title screen
5. Reload the world,

And the horse will disappear, happens every time I do it.

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Code analysis by Marcono1234 in this comment