The weather, along with the image of the horse, reminds us of the terrifying force nature can have, and its wild unpredictability.
At the beginning of the story, the rain is slight-
The first thin blowing of rain met him.
The man is already out of his depth in this landscape, and we know that the situation will get worse, as nature seems to view him as an unwelcome intruder
He had come too far.
The rain is given living qualities, having an immense strength as is approaches again-
He saw the rain pulling up out of the distance, dragging its grey broken columns.
The rain is, however, more anthropomorphised than personified: its living qualities are far more animal than human.
The man appreciates the way in which the rain seems to suspend time, but he is unsettled by the horse watching him, standing unnaturally out in the rain. Once the horse attacks him, the rain becomes more dark and intense, adding to the fear and threat posed by the horse. The rain makes the sodden ground even more difficult to negotiate, and the horse harder to see through the grey deluge.