In the spirit of full disclosure, I should say that all my early riding training was in American hunter seat, and that what I pursued certification, it was with the ANRC (Affiliated National Riding Comission) and organization that promotes and teaches Littauer's vision of forward seat riding.
I am a passionate advocate for the true American system of forward seat riding. No, that does not mean I advocate jumping ahead, laying on the horse's neck, the floating faux crest release, or the hollow backed, duck butt posture and more than anyone else advocates for the worst characteristics of their chosen discipline. I advocate for a freely forward moving, relaxed, obedient horse doing his job with as little interference or influence from his rider as possible, as close to his natural balance and movement as possible.
I came to eventing and jumpers later in my career, and I approached both endeavors from the perspective of that early forward seat background.
I once asked a famous eventing clinician why eventers couldn't ride everything from a two point, and why they looked so awful riding drops. His response was "Because no Italian (Caprilli) ever won the Grand National." More about that later.
I'm going to stop there and address a point mentioned earlier, the idea of the importance of seat as an aid. Sorry, and I know this is going to upset people from dressage backgrounds, *your seat is not an aid in forward seat riding* period. There is some place for a full following seat, but no place for a driving seat or your seat as an aid. Your weight may be an aid, but your seat is not. The idea is that you have a horse that moves freely forward NOT held between your leg and hand, and that if you have established, pace, balance and direction correctly, you do absolutely nothing in the last three strides before the fence. This last bit is a concept I have heard repeated over and over by eventing instructors and clinicians, including some from the UK. Some riders, especially those with a strong dressage background, are just very reluctant to give up that seat to hand connection, but ultimately, I believe dependence on that seat to hand connection robs the horse of his ability to think for itself and jump his rider out of trouble when they inevitably make a mistake.
In an earlier thread on this forum about making the transition from American hunters to eventing, I summed up the various points by saying "Riders from an eventing background keep themselves in the tack unless circumstances dictate that they come out of it, riders from a hunter/forward seat background stay out of the tack unless circumstances dictate that they stay in it/take a deep seat." I have a pretty firm conviction that that's the better way, and I recently got support from and unexpected source.
Jimmy Wofford wrote an article in the August 2011 Practical Horseman called "The Science of Galloping" in which he referenced a 2008 Royal Veterinary College study which concluded that the workload on a horse was greatly reduced in the rider assumed a balanced, flexible galloping position out of the tack as opposed to seated in the tack.
Obviously you want to assume a defensive position jumping down banks, jumping into water, jumping downhill or in a tight, very technical combination where you need a lot of influence over the horse's stride. However, you are saving your horse work if the rest of the time, you are out of the tack, in a poised, balanced flexible two point position.