In order to see what's going on, let's put them in empty space to get rid of any other influences, and let's also make it a push instead of a pull. / / / The horse pushes on the cart, so it begins accelerating away from him. At the same time, because of the equal opposite reaction thing, the cart pushes back on the horse, so the horse starts accelerating backwards, away from the cart. They both accelerate in opposite directions from where they started. BUT . . . their common center of mass doesn't move, and the sum of their momentums (which are in opposite directions) remains zero.