What happened is not immediately apparent. I'm guessing that Horse - his proper name - has poor eyesight, and took a spill; this resulted in Dudley sustaining several injuries, as well as damage to their hats. Horse did not emerge unscathed; hence the bandaged leg, which probably means he will have to be shot.

Or not. The veteranarian probably isn't very good in the first place, because he put a small bandage on the beast's coat.