They survive yet?
I mean the medieval "destrieri" used in battles during middle ages, or now they are all imbastardized with the arabic ones?

when you say: historical accuracy. :D

For one thing, we're not sure about the exact breed(s) of horses used by medieval men-at-arms.

For another, it is very likely that even the earliest medieval warhorse breeds were already warm- rather than cold-blooded; the hot-blooded horses from North Africa and the Middle East were already well known since Roman times, and horse trade seems to have resumed at least as early as Charlemagne's reign, which would have given horse breeders plenty of time to "bastardize" their breeds in order to combine the energy of the hot-blooded breeds with the strength and steadiness of the cold-bloods. Or at least that's what the modern Spanish-Norman horse breeders think.

There's still a good deal of debate over what medieval warhorses even looked like. Matthew Bennet's article, "The Medieval Warhorse Reconsidered," is probably the best introduction to the subject.

Even the concept of breed is somewhat anachronistic if we're talking about the Middle Ages. Medieval people referred to horses by types, e.g. warhorse, packhorse, cart horse, etc., and individual horses might be distinguished by their places of origin, e.g. "my Spanish horse," but they didn't maintain breed studbooks the way later horsemen did.