This poster from the Akira Kurosawa film Kagemusha illustrates the classic view of early samurai cavalry. Great cavalry charges of thoroughbred looking horses.
But as Karl Friday in his book Samurai, Warfare and the State in Early Medieval Japan reveals, the mounted samurai of the movies bare little resemblance to the actual mounted warriors from medieval Japan. Early medieval Japanese war-horses were actually much smaller and slower than the horses seen in classic samurai movies.
According to Friday, the mounts favored by early medieval samurai were stallions raised in eastern Japan and selected for their size and fierce temperament. They were stout, short-legged, shaggy, short-nosed beasts, tough, unruly and difficult to control.
In 1953, a mass grave at Zaimokuza near Kamakura was unearthed that is believed to contain the remains of men and horses killed during Nitta Yoshisada's attack on the city in 1333. The skeletons show the horses of the period ranged in height from 109 to 140 cm at the shoulder. Modern thoroughbreds by comparison range in height around 160 to 165 cm.
Also, these medieval horses could not sustain high speeds for long distance due to their size and the weight they were carrying, mounted samurai with full armor. Even modern racing horses can only go full out for 200 or 300 meters. Early medieval Japanese horses gave the samurai a rugged, stable, and comfortable platform from which to shoot their arrows, but it was a heavy beast not well designed for high speeds or long distance riding.
So the scenes in the movies with the cavalry charges that seem to go on forever are of course greatly embellished. But they make for an exciting movie.