Simple Steps to Training the Rider's Core

shoulders and your legs. Many riders with pulling hands often have weak core muscles. The pulling hands are the bodys compensation for its inability to stabilize the position through the core.
I consider the riders core to be a foundational training area similar to the first levels of the training scale used in dressage. If you do not ride dressage think of a scale of tasks your horse needs to be competent in before he can move to the next level. All horses need to move with good rhythm. Even though it is a factor from a very early stage you never get beyond it it is always important. If your horse gets to a higher level in his training and loses rhythm then you have to go back down to basics. Core strength for the human athlete is similar because without it your body starts to use compensating motion patterns to perform tasks you ask of it. Compensating motion patterns cause hypermobility or stimulation of other muscles which causes muscles and joints to be used more than they were meant to be or in movements they are not best suited for. This introduces unnecessary wear and tear on that area. For example a rider with stiff hips and weak lower abdominals will have a tendency to absorb more of their horses motion in their lower back which can lead to pain and strain over time. 
Another common example is the rider who has a weak core and is not maintaining correct pelvic position. As a result the horses motion causes the rider to lose balance a little which their body manages by tightening their inner thighs. This rider may have to use artificial aids to induce the horse to move because the tight inner thighs create leg pressure that becomes white noise to the horse and so he cant hear normal leg pressure anymore.
The importance of training the core for a rider just makes so much sense. In fact when I am working with clients who are under time pressure I will frequently advise them that if they have to drop exercises from their schedule in a given week or during a hectic show season the two activities they should keep without fail are exercises for flexibility and core strength. One reason is that both stretching and core work can be done anywhere anytime and while wearing just about anything which makes it really easy to keep them in your life when you are extremely busy.
What is less clear for many people is exactly what to do about core strength. Its not as easy as just saying Work your abs. When I am designing a training program at a clinic or for a private client I will emphasize different exercises and degrees of core training that depend on several factors
the individual age fitness level physical issues
discipline requirements for example crosscountry fences introduce much heavier demand in more directions on a riders back than other events
the amount of time and tools available to the rider for training.
However most riders can benefit from any core training as long as it is wellrounded enough for a rider consistent and keeps them interested in doing it faithfully. To get results you also need to always push the envelope just a little bit further each time you work out.
Most people can have a noticeable impact on their core strength by starting off with five minutes a day of training. Because core muscles have a lot of endurance time is your best ally in training and you must use it if you want to avoid injury.