Horses change, so make sure that his harness is not only still correctly fitted but that he is comfortable in it.
He may simply need to build muscle so that he can haul the cart easily. They have to push all that weight forward with the bottom part of their shoulder with each stride and that takes strength that must be built through work. Have you been driving him in deep footing? That would also cause more drag and less reach with the forehand.
Bigger horses will have longer strides, yes, and often better scope, but not necessarily more extension. Just being tiny by itself does not prevent them from extending well. It's the conformation that often comes along with being tiny that may limit the stride and larger horses can have those same problems.
As far as exercises, drive him very "forward" at all times. Don't worry about his head for now, just try to do a lot of long trotting (not long duration, long frame) and encourage him to move out with soft support on the bit. Get the forward motion first then you can refine it into a collected frame. Do big three-loop serpentines, encourage him to move out across the diagonal of the arena when changing directions, do many quiet transitions from walk to trot and back again to help build his muscles and rock him back on his haunches more. Reward any sort of long, rhythmic trot until he gets the idea. But first and foremost make sure he's comfortable. That is the single biggest reason why a horse won't move out.
Leia
Edited for typos