When a horse pulls a cart, by Newton's III law the cart also pulls the horse with equal and opposite force, then how does the motion of horse, cart and system takes place?

When a horse pulls a cart, the force that helps the horse to move forward is the force exerted by

When a horse pulls a wagon, the force that causes the horse to move forward is the force

when a horse pulls a cart, the force that helps the horse to move forward is the force exerted by

When a horse pulls a cart, the force which is responsible for the movement of cart is

A horse is urged to pull a wagon the horse refuses to try, citing Newton's third laws as a defense: the pull of the horse on the wagon is equal to but opposite the pull of the wagon on the horse. "If I can never exert a greater force on the wagon than it exerts on me, how can I ever start the wagon moving ?" Asks the horse. How would you reply ?

According to Newton's third law each team pulls the opposite team with equal force in a tug of war. Why then one team wins aned the other loses?