(a) Yes. It is important to notice that this case involves what is called a latent (hidden) ambiguity. The terms of the written contract seem clear enough on their face, but when it turns out that there are two horses called Mayfair, the contract could be referring to either one of them.
Such cases are treated as an exception to the parol evidence rule and evidence may be led of oral terms that resolve the ambiguity. It is important to notice that it is the identity of the thing that is uncertain, rather than its quality. Uncertainty as to quality does not justify the same exception.