There is one lady, who runs an equestrian club, her name is Peggy. On Sheikh Faisal's farm. The stable is perfect with a sitting area for families, refreshment area, and two covered rings to shield you and the horses from the sun. It is near the came race track. Im not sure about jumping, but if you are advanced, you can proceed to Al-Shaqab, but you can always ask her to arrange something for you.

She charges around 75 riyals per half- hour.