The atmosphere of "The Rain Horse" by Ted Hughes is, indeed, rather gloomy and dark, even mysterious. Hughes begins to set this particular stage even in the very first sentence.

The initial method Hughes uses to create this oppressive atmosphere is his depiction of the weather. The man (the unnamed protagonist) is met with a "thin blowing of rain" which will soon turn into a downpour. He surveys the muddy ground below and "now there was a raw, flapping wetness in the air that would be downpour again at any minute." The rain, consistently symbolic of gloom and depression, is a continuous presence in the story. While a spring rain might be refreshing, a consistent downpour is oppressive and often serves to distort reality in some way. This rain also sets up a conflict between man and nature, adding to the dark and oppressive atmosphere. 

Hughes continues this atmosphere by the emotions he gives to the man. At times he "felt nothing but the dullness of feeling nothing." At other times he feels as if anxieties are swarming him, and then "[a] wave of anger went over him: anger against himself...and anger against the land." These mixed emotions, none of them positive, also serve to increase the dramatic tension of the story.

The terrain is also part of the specific atmosphere Hughes is trying to create. 

Now the valley lay sunken in front of him, utterly deserted, shallow, bare fields, black and sodden as the bed of an ancient lake after the weeks of rain.

This depiction of a barren, black terrain suits the gloomy and rather mysterious tone of the piece. Even more, it sets up the idea of the unnatural which is to come. We know that a lake bed is supposed to hold a lake and fields are not generally supposed to be bare; this land, though, is not able to do what it was designed to do--a foreshadowing of the horse and his unnatural behavior which is to come.

Finally, Hughes does an effective job of creating this atmosphere of mystery, gloom, and darkness is his first description of the horse. We already see that the man is set up in opposition to nature in the form of the weather and the terrain. Now we meet the next form of nature which is likely to present some opposition to the man: the horse. The first description we get of the running horse is this:

It seemed to be running on its toes like a cat, like a dog up to no good.

Again, this is not the natural behavior of a horse, and this is one more unnatural element which contributes to the already threatening atmosphere of the story. Though we do not know exactly what is in store for this unnamed man, we know that it is not going to be good because he is already distraught, and now everything he meets (weather, terrain, horse) is in some kind of opposition to him. 

What are some techniques Ted Hughes uses for atmospheric effect in "The Rain Horse"?

As a poet, Ted Hughes uses language in a very specific manner; strong descriptions and simple, unadorned prose allow deeper meanings to come from his texts. In "The Rain Horse," it is the power of his descriptions that creates most of the atmosphere:

The wood hummed and the rain was a cold weight, but he observed this rather than felt it. The water ran down inside his clothes and squelched in his shoes as he eased his way carefully over the bedded twigs and leaves. At every instant he expected to see the prick-eared black head looking down at him....
(Hughes, "The Rain Horse," Amazon.com, emphasis mine)

By showing the wood with dripping cold rain and close trees, "bedded twigs and leaves" and the ominous specter of the attacking horse hanging over him, Hughes creates a sensation of claustrophobia. A forest is normally a wide-open, immense space, but the man has nowhere to run because he feels the wood is alive, waiting for him to trip up or stop running. Hughes uses powerful adjectives and nouns to create a living space rather than a simple description. The wood here is not just a place for animals to live in, but a hostile force of its own, impeding the man's progress and wearing him out with brambles and the constant rain.

How does Ted Hughes create atmosphere in "The Rain Horse"?

Ted Hughes uses strong descriptive language to create an oppressive atmosphere in "The Rain Horse." As the unnamed man is attacked by a relentless horse in the woods, he is beset by both the horse itself and by the rain:

He saw the rain pulling up out of the distance, dragging its grey broken columns, smudging the trees and the farms.
[...]
As he watched it, the horse ran up to that crest, showed against the sky -- for a moment like a nightmarish leopard -- and disappeared over the other side.
[...]
In blinding rain he lunged through the barricade of brambles at the wood's edge. The little crippled trees were small choice in the way of shelter, but at a sudden fierce thickening of the rain he took one at random and crouched under the leaning trunk.
[...]
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... then he was away up the slope, whipped by oak twigs as he leapt the brambles and brushwood, twisting between the close trees till he tripped and sprawled.
(Hughes, "The Rain Horse," Amazon.com -- emphasis mine)

The bolded words and phrases show how Hughes uses language to create a small, oppressive place where the man is trapped. He has nowhere to go because of the "close trees" and "barricades of brambles," and the "blinding rain" keeps him from seeing further. The horse is a ghost, attacking with guerrilla intensity and without reason or purpose. Each powerful phrase and metaphor shows how small and helpless Man is against Nature, and how Man must strive to survive in an unreasoning world.