there is no way to remove the armor or saddles from a horse once you placed it.
this is very annoying if you have a beautiful horse and you want to see it without the armor or saddles.
Linked issues
is duplicated by 1
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This is still an issue for me in 13w16b. This not only prevents viewing of a naked horse, it also prevents breeding with these horses I just rode ~10km to get back to my house in SSP. Help would be appreciated.
Can confirm for 13w16b.
Do me a favor and include saddles. It Holds for them as well and my report was closed as duplicate of this. In my opinion saddles and armor are not the same.

Done
This is not a bug, Mojang has said several times that this is intentional as of now. They plan on adding it further down the road. Please check the Minecraft Wiki before posting an issue.
The Minecraft Wiki is not written by Mojang, Nathan. They have never said it was intended.
Correct, Elias, but Jeb tweeted this fact after being spammed by people screaming at him.
Is this still a concern in the current Minecraft version? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.