This post is to address a very common trope - for which I entirely blame Tolkein.
The trope is the super magical horse being ridden with no tack - usually, but not always, by an elf. It's either because the super special magical horse won't take harness or to show off some kind of amazing magical natural horsemanship.
I am pretty sure everyone who writes this has never ridden bareback.
There are three purposes to the saddle (and these hold regardless of the saddle style):
1. Safety - to reduce the risk of a fall.
2. To make riding more comfortable for the rider.
3. To distribute the rider's weight better, most especially to keep the rider from direct contact with the horse's spine, in order to make things more comfortable for the horse.
So, any sane sentient, magical horse would want their rider to use a saddle. Mercedes Lackey gets this right in Valdemar - although Heralds train bareback, they always saddle their Companions for battle or lengthy rides. The same goes for demonstrations of fancy horsemanship. In addition - and I'll talk more about this in another post - stirrups are very useful if you're fighting from the saddle.
Now, you might not use a bridle - that's a different matter. A sentient horse probably won't want to wear a bit - although a mounted warrior might still use a bridle or headstall of some kind to support head armor. And bridleless riding is used as a demonstration of amazing horsemanship and/or training routinely to this day.
But bareback is something riders generally wouldn't do for more than short periods - it is useful for training stickability and everyone's hopped on their horse for five minutes without a saddle at some point. You just don't want to do it for long periods of time - it's simply not fair on the horse.
Trail horses saddled and ready to go.