HUnters is all about form and ease. Even if yourt horse is a nutjob (I know yours isn't) you want to make them look smooth, consistent, and easy with tight kness and proper striding. You want the judge to think I'd love to ride that horse.
For the flat class you do a half seat to stay off the horses back and let your horse move underneath you without you interference, plus loose reins. As far as movement, the horse should have flat knees, be floaty and most judges love the ones that kind of "flick" or point their toes. A steady rythym and a good expression on the horse help alot. You want the horse to have a low (but not real low) head and point their nose out a bit. A vertical or horizontal nose is not good though.
For jumping, You need to use your corners, jump the middle of the jump, and have smooth flying lead changes. YOu have to get the correct striding between jumps and try to get the perfect takeoff point. Tight knee, good use of the neck, and a steady rythm (no running down the lines)
I agree the athletic ability of a horse is tested more at eventing/jumpers, but people underestimate the work put into a horse to get the steady, efforrtless look of a hunter. If you think it looks easy, great! The rider is doing their job