If action is always equal to reaction, explain how a horse can pull a cart ?

Explanation

Consider a cart connected to a horse by a string. The horse while pulling the cart produces a tension T in the string in forward direction. Tension acts as action. The cart, in turn, pulls the horse by an equal force T. in the opposite direction.
The horse initially presses the ground with a force Fin an inclined direction. Earth exerts equal and opposite reaction R on the horse. The reaction R can be splitted into two components such that:
i) The vertical component V which balances the weight W of the cart.
ii) The horizontal component H makes the horse to move forward.
As horse moves forward so `H gt T` . In this case, net force acting on horse= H-T.
Let a is acceleration produced in horse, then ma = H-T where m be the mass of horse. The cart moves forward if `T gt f` where fis friction between tyres of cart and road. in that case, net force acting on cart=T-f. If Mis mass of cart then acceleration of the cart is a.
Then Ma= T-f ....(ii)
Adding (i) and (ii)

`(M+m)a= H-f` or `a= (H-f)/(M+m)` It means, a is positive if H-f is positive or `H gt f`
Thus the system moves if `H gt f`