The Mouth of Sauron did not ride a horse in the books. At least I've never heard of a horse with flames instead of eyes!
With regard to orcs riding horses, Tolkien describes them as being bow-legged, which might make horse-riding a little complicated, but otherwise horses have no loyalty and would easily be used for a multitude of purposes. Sauron might well send spares to Harad and Rhun, or to equip the Minas Morgul cavalry.



