What is the fence?

The fence in “The Barn at the End of Our Term” is representative of the lack of acceptance being found among the horse-presidents. The fence surrounds the pastures where the horses graze, and becomes the chief obstacle to escape. Only James Garfield has ever been able to leap the fence. Rutherford B. Hayes eventually comes to accept that just because the farm may be escaped, doesn’t mean his new identity as a horse can be escaped. Upon accepting this, he is successfully able to leap the fence.