Core strength is a particularly important aspect for all equine disciplines. As your core muscles are at the centre of your body they help support your spine and hips. These muscles are therefore important to riders for a variety of reasons:
Having tight core muscles allows for all of the muscles surrounding your spine to be stable which in turn allows you to move effectively with the horses movement. Without a strong core this can lead to lower back pain and potential injury as the ligaments and tissue surrounding the spine can become overworked.
Many top riders appear totally still when riding their horse, particularly in dressage. this often comes down to the riders core muscles. Having a strong core will support your back and keep you positioned correctly. Strong core muscles also can prevent you from having to grip with your knees and balance on your hands as you will move less.
Less risk of injury
If your core muscles are strong this will allow you to be correctly positioned therefore allowing better balance. This will also allow you to move with the horse. This means that in the event of a spook or if the horse trips, you are more likely to move with them than you are to fall off. However, your core will also help should you fall off as the strong muscles will help protect your neck, back and hips.
Here are some exercises demonstrated by Leon Munce to help strengthen your core:
Hanging leg raises