If a horse pulls a cart, the force that assists the horse in moving forward is the force exerted by:

The horse moves forward in a forward direction. 

As we all know, reaction forces are always found in pairs. As a result, if the horse applies pressure in the negative X-direction, as shown in the diagram, the ground will respond with a force of equal magnitude but opposite direction on the horse. This push assists the horse in moving forward. The force pulls the cart forward as the horse moves forward. As a result, the horse's movement is caused by the ground's force. The frictional force is the name given to this force.