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.
I didn't know it like that, but I agree that it's better. The version I first read in the early to mid nineties was much longer than this one though, and his achievements at quick wit retort just went on and on from one unbelievable accomplishment to the next -- which of course makes the punch line that much funnier. The version I remember was also quite elegantly written, which made the crudeness of the last line that much funnier.
Speaking of things that are funny to some and not others, an instructive example is the Orange Head joke. Usually when it's told, the audience is sharply divided into those who think it's hilarious and those who struggle to see what's funny.
Here's the Orange Head joke:
Do you think it's funny?
If you search for this joke's key words, you'll see many pages where, after it's told, people react incredulously and ask where the joke was. Others at the same time are laughing their heads off. Here's a blog post that attempts to analyze this, though it doesn't get far.
(I personally think it's hilarious, and easily the best joke I heard last year. When I retold it at my blog, I got many concurring comments, but also comments from people who didn't see anything funny, even after those who did tried to explain what they found in it. Several people went on to convince themselves it's garbled and there must be an "original" version in which the final remark makes sense and is funny - and offered several ideas of how it might go).