In "The Rain Horse," the obvious example of the Pathetic Fallacy, in which non-humans are ascribed human emotions or motivations, is the titular horse itself. As the unnamed man flees, he sees the horse as making decisions about how to hide and spring out to attack. After the second attack, he decides that the horse is "definitely after him," and changes his strategy to cope with an apparently thinking creature.
There are also examples in the descriptions of the wood, which is almost alive in its hostility towards the man:
He saw the rain pulling up out of the distance, dragging its grey broken columns... The little crippled trees were small choice in the way of shelter... he was away up the slope, whipped by oak twigs as he leapt the brambles....
(Hughes, "The Rain Horse," Amazon.com
The forest and elements are actively involved in the story, "dragging," "whipping," and the trees are "crippled." Although he doesn't feel as attacked by the forest as by the horse, it does nothing to assist him except for providing inadvertent cover.