The hand-axe may be too short a weapon. Historically, horsemen tended to use longer single-handed weapons than infantry. And, if you're close enough to an enemy that the rearing isn't a display move, I think you need to consider where the enemy is and what he's doing to get that reaction. Unless he's getting a faceful of forehoof, that doesn't look like a fighting pose. (Speaking of horsemen, have you noticed that trick Karl Urban pulls off during the first charge of the Rohirrim?)