I suspect this may have more to do with film riders being uncomfortable riding galloping horses with the shield and the reins held in the same hand. It looks as if the shield has been strapped to the saddle for convenience, rather than for any protective purpose. While I'm certain that medieval horsemen would have carried their shields in similar ways when out of combat, I have never seen anything to indicate they went into battle in such a manner. It doesn't make much sense - you would want that shield up and facing out so as to protect your vital bits.