Ted Hughes is the author of the short story, "The Rain Horse."

In terms of conflict, it is defined as...

The opposition between two characters (such as a protagonist and an antagonist), between two...groups... or between the protagonist and a larger problem such as forces of nature, ideas, public mores...

Two obvious conflicts are man vs. nature—an external conflict: as seen with the man struggling against the rainstorm and the horse.

The rain is at first a curse. The unnamed protagonist cannot abide the weather, which is ruining his new suit and shoes. The other conflict of nature is the "rain horse," which several times attacks him:

...the ground shook and he heard the crash of a heavy body coming...the horse was almost on top of him, its head stretching forwards, ears flattened and lips lifted back from the long yellow teeth. He got one snapshot glimpse of the red-veined eyeball...

There are other elements of conflict in the story. The first is man vs. self—internal conflict. After twelve years, the young man has returned to the region he knew growing up. He is disappointed because he expected to feel something—but he feels nothing. (Perhaps he hoped things there were not as bad as he remembered them.) His attempt to avoid the farm as he trudges through the storm also shows another conflict (man vs. man—external conflict):

...the thought of meeting the farmer—to be embarrassingly remembered or shouted at as a trespasser—deterred him.

A final conflict, which gives us the sense of an "other-worldly" element, is found in the seeming sentience and purpose of the horse. This is external conflict: man vs. the supernatural (or, some would say, "God.") "Supernatural" does not refer to ghosts or aliens from outer space (in the strictest sense), but to anything beyond the natural world. This horse chases the man. He watches him. He attacks with intent.

...the black horse was standing under the oaks, its head high and alert, its ears pricked, watching him...this last attack had cleared up one thing...It was definitely after him.

The rain may symbolize his past and the horse may be symbolic of facing the past. With all the kinds of conflict present, it is clear that  in total, the conflicts facing the young man seem to come from this land, this farm, and they are overwhelming. He looks at the farm and wishes to remain in the rain...

...to take the cooling, healing drops all over his body and forget himself...

"Healing" infers "wounding." The countryside now looks "lifeless and desolate," perhaps reflecting the young man's inner-pain and suffering. 

One source notes that of the two opposing forces in conflict, one must overcome the other. In this case, it would seem that the conflicts raging within and around the young man overcome him at the end, and he sits in the shed—surrounded by memories—like he is stunned...perhaps even hopeless.