If these are just your first attempts, I'd say you're off to a very good start. Rather than waste a lot of words here, I'd point you to a set of good,
free video tutorials on sport photography. Even though these are aimed to cover traditional American sports, a lot of the techniques also apply to equestrian events. Scott Kelby's tutorial on the aforementioned link provides a good overview.
Sports photography is very demanding on equipment, but don't be discouraged if you don't want to throw a lot of money at it.