Having spawned and renamed a Donkey and a Mule, I can no longer ride them. They are equipped with a saddle and a chest, but pressing the 'Ride' button does nothing unless I'm holding a saddle, in which case it just opens the mounts' inventory. I am able to feed them and breed them.
I can't add steps to reproduce this issue at the moment, as it appears to have happened randomly, but will update the description when I find more information.
Since 0.15.0 build 2, one of the horses can now be ridden, the other still cannot.