The horse pulling the waggon can move forward due to:

When a horse pulls a waggon, Newton's third rule of motion states that the force that causes the horse to go forward is the force exerted on it by the earth.

If  a horse pulls a waggon, the ground is pushed backwards by the horse. The ground exerts a forward force of equal magnitude due to the third law of motion. The waggon travels forward because the rearward force applied by the vehicle is less than the force applied by the horse.