|MadSci Network: Physics|
This is a common misunderstanding with Newton's Third Law. The most common natural-language expression -- "for every action, there is an equal and opposite reaction" -- is badly written for comprehension. A better version (as suggested by Wester's World) would be:
Whenever one object exerts a force on a second object, the second object will exert an equal and opposite force on the first object.
The important thing to note is that each object is acting on the other object, so the action and reaction do not cancel each other out. They just affect different objects in the system.
In this example, when the horse acts upon the cart, pulling it forward, the cart reacts by "pulling" back on the horse. The cart does not pull on itself! So while the horse's action is pulling the cart forward, the cart's reaction is making the horse tired. You can also check out a similar example involving one airplane pulling another.
For more fun with Newton's Laws of Motion, read this tutorial and play with some online experiments (you'll need a Java-enabled browser for the latter).
Hope this helps!
Try the links in the MadSci Library for more information on Physics.