This sounds like what I had during my Mounted Combat mod implementation.
The problem is with new behavior/animation states conflict.... So the 'mod' that causes is FNIS
I don't think uninstall this mod should fix it for you, you need to remove the files under
Steam\steamapps\common\skyrim\Data\meshes\actors\character\behaviors
Since 1.6 update, FNIS is incompatible with Skyrim new behavior system. You might want to check with the author to make sure he changes the behavior xml files accordingly as of yet