Forward Seat horses are TRAINED to the Forward Seat method. If they are trained to a more abusive method of jumping, yes the horse will be extremely leery of anything a rider does that is out of their previous comfort zone and will suck back just waiting for the rider to abuse them with hand, leg and seat.
Back when I was training my Anglo-Arab to jump using the Forward Seat method AS A COMPLETE BEGINNER TO JUMPING (both of us were beginners to jumping) he never refused a jump. We ended up jumping 3’6" regularly .the ring, in the field, and any odd jumps we ran into on the trail.
Of course I followed Littauer all the way. By the way back then I often rode without anybody else around since I worked odd hours, 2nd shift.
There IS a difference between a proper Forward Seat and the riding that all too often puts the horse completely on its forehand. The horses know the difference and believe me these horses will often react appropriately to Forward Seat riding, especially over the jumps.
Modern competition dressage riding makes me SICK. I want to run into the ring and save all those poor horses from the abusive riding that they suffer. In over 50 years of riding I NEVER poked a hole in the side of my horse with my POW spurs and I NEVER caused the horse’s mouth to bleed. I may not be able to get a piaffe but i can turn horses who are super unwilling to move forward at all into free striding happy horses who are content to keep contact with my hands with their faces ahead of vertical, even though I am crippled with MS with problems with my hands, legs and balance.