Sometimes, when you log in a world, tamed horses (and possibly untamed ones, i don't know) will disappear, and if leashed, the leads disappear as well. You can fix this by re-logging, but it is still annoying. I first came across it on my custom-world survival world, and it seems to be (possibly important info ahead) only horses I tamed in survival. I don't know for sure if its only horses tamed in survival, but those are the ones disappearing. Please fix, thank you, beautibird.