That joke is like the Aristocrats insofar as it's an opportunity for improvisation (at as great a length as you can get away with). Also analogously, I've usually heard it as the "'Fuck you, clown' joke" (or just the "clown joke" if you really care about spoilarz).
And in the versions I've heard, the clown calls the guy down to the stage, and asks "Sir, are you a horse's head?" "No." "Are you a horse's leg?" "No." "Are you a horse's tail?" "No." "Well then, it seems to me that you must be a horse's ass!" which is both funnier (to me) and (importantly) longer.
Yes, that's how it should be.