I saw a donkey with its ears missing in a normal survival world with no texture packs.
I minimized the game then came back, and the donkey's ears were back to normal.
I attached a screenshot.
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I am on windows 10. Using version 1.6.1 of Minecraft.
I figured a way to bypass it. so u need to uninstall the game from system and reinstall it. once i did that i haven't had problems since. PS your worlds should still be there mine were. also i was the one who made this report and fixed issue myself.