That is a question that I've won a lot of beers with. By the principles of physics, the horse is pushing the cart. All the same muscles used in pushing are in use and, even though the object is behind the horse, the weight is in front.
He's pulling, by means of pushing into the straps. But I have to be with the group that says cause he's in front, he's pulling. Much like a vehicles tires PULL a horse trailer by pushing on the ground to move in the first place. I think I'm a simple person-if the power is originating in front of the object to be moved, then the object is pulled. If the power is behind, then it's pushing.