In saddleseat riding, the balance of the horse is shifted towards the rear, so one does sit further back, however the straight line from ear, shoulder, hip ankle is the same.

Many people find it harder to ride correctly in a lane fox (saddleseat) saddle (no padding, knee or thigh blocks), so that is why you may see more people with their legs pushed forward.

The OP is riding HP and WP, so the balance of the saddle/horse tends to be the same as any other.

When riding any more "uphill" breeds, morgans, ASBs, some arabs, and other baroque-type horses, a properly trained horse should shift it's weight to the hind end and raise the front end, but in a perfect world the rider wouldn't really be affected.

But, since we all get older and less focused on EQ, we let things slip