You can ride a horse bareback, but it is generally best to use a saddle. Saddles, although functionally about the same, come in different types, such as English saddles, pony saddles, treeless saddles, and others.
Saddles are usually leather but sometimes synthetic materials. They're lightweight and sturdy, to rest easy on the horse or pony. Saddles are part of the essential horse tack along with bridles, bits, and reins. Keep the girth tight on your saddle.