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Well, Shadowfax in the book was ridden bareback with neither reins nor saddle, but it just wouldn't be safe to put even an accomplished rider bareback on a stallion and expect to have the kind of seat necessary to stay on and control the horse through required fast movements. And there would be no way that a non-rider like Ian McKellan could do it safely. So they cheated. It is visible only in a few shots (the one above is an out-take)

Giving the rider a small saddle under there is a perfectly acceptable cheat. The amount of extra training they had to go through to get that horse working without bridle was difficult to accomplish. They could have easily skipped that detail about Shadowfax and not had many people complain. But they did it.