This is very interesting. Besides Oakshott's book does anybody have any cites for information on this?
It's kind of everybody's guess. I know there was one book by the Museum of London about some excavation finds, but I think it is out of print. Another out of print book is The Medieval Warhorse: Origin, Development and Redevelopment
by Davis, R.H.C. The only cite I know of supporting Oakeshott's opinion is Ann Hyland's "The medieval warhorse:From Byzantium to the Crusades", a book, however, that is a prime example of what harm amateur scholarship can do if running amok. Hyland is a horse lover and breeder, but has practically no training as a historian, or scholar for that matter. As such, she frequently relies on translation of dubious quality, jumps to conclusions long abandoned by academic research, and her book has been shredded in some academic reviews.
One thing I find interesting is the so-called "Spanish-norman" breed, an attempt at re-breeding the warhorse by crossing the andalusian (small, fast, typical courser) with the Percheron (French draft horse) while keeping it at a 50% Andalusian minimum. Interestingly, these horses are MUCH larger than Andalusians (average height 17 hands) while not as slow as the Percheron. Andalusians are known to have been prized horses (William the Conqueror was famous for having received one as a gift) but were extremely expensive, and so probably not in too widespread use. It is interesting to see that even a fraction of Percherong genetic stock is able to increase the size of the horse considerably.
I think one problem people frequently make when dismissing the type of Belgians and Percherons is that most of them have been bred to draft horses only in the last few centuries. The fact that they claim
descent from warhorses doesn't mean any claim of warhorses looking and behaving precisely like them. On the other hand, they are also frequently underestimated. Frisian horses, for example, are even used in dressage sport and as such can be quite agile. At the same time, they can pull carts and carriages.
I am not quite sure what the current state of academic research on the issue is, but the last discussions I was aware of made the whole issue close to a philosophical question, with discussions lacking any real HARD evidence either way. I'm no historian myself, though, and have no access to recent academic journals in the field.