This link contains both factual and implied errors.
First, although horses do posses sufficiently powerful hind legs, it is unlikely that they would be able to stand as depicted in a jocular fashion.
Secondly, horses more than likely, do not posses any innate compositional ability or synchronisation skills. This renders the fact that they can sing harmoniously a unlikely assertion at best.
Finally, the fact that horses would attempt a barbershop quartet, even providing them with the intellectual capacity to do so, is considerably dubious, as they lack the social background to be fully aware of what is meant by barbershop.
All in all, a false representation of the equine community.