Why don't airliners have rudders on the winglets?
The purpose of the rudder is to control the heading of the aircraft. It turns the aircraft by creating an aerodynamic moment about the vertical axis of the aircraft. The moment is product of the aerodynamic force and the arm. 



image: NASA

The aerodynamic force is the the side force on the rudder, the arm is the distance between the rudder and the centre of gravity of the aircraft. 

If the rudder would be on the winglets, the side force of the rudder would act at a short distance behind the centre of gravity, reducing the effectiveness very much. 

It would be possible the have airbrakes on the winglets / wingtips and use differential braking to create the rotating moment. This is done for example on the B2 which doesn't have a vertical stabilizer. The added complexity and weight increase makes it an unattractive option for conventional aircraft.