A horse has to exert a larger force initially in pulling the cart because, the force of limiting friction is larger than force of kinetic friction. Initially when the cart is at rest, horse has to overcome the force limiting static friction to move the cart. But once it started to move, horse has to overcome the force kinetic friction only. That is, Since the force of limiting friction is larger than the force of kinetic friction, horse need to pull harder during the first few steps.