Question

"A horse is pulling a cart. According to Newton's third law, the cart is pulling backward on the horse with a force equal to the force with which the horse is pulling forward on the cart. Why don't these two forces cancel out , thus making it impossible for the horse to pull the cart?"

Our professor brought up this question in class for discussion, and we ran out of time. Can someone explain this question to me? Logically I know the horse is able to pull the cart, but I'm absolutely stumped on how to answer this the "physics way"!