Lots of worlds already have giant animals to ride. I cannot think of any where people use smaller than normal animals to ride. But this would offer a lot of story telling perspectives. For one it would be easier to feed your mount and take it inside if it were the size of a cat, because it was a cat. You would need to make these mounts supernaturally strong, which can be from the wizard breeding project. Riders would need a good sense of balance, or possibly one mount for each foot. Several mounts distributed about the body would be more secure and less weight for the mounts, although you might need to travel recumbent.
This gets even trickier with flying mounts. Underconfident flying riders might have their (I mentioned they were strong) mounts carry them hanging below, perhaps by the hair or their collar. This sounds like the sort of thing witches would do.
I like very much the idea of the faerie lord coming across the water at speed, holding one foot behind him with his hand. He stands on the back of a fish which is just bigger than his bare foot.