Figures of speech are words used in a non-literal sense. In this poem, Frost is using literary devices or figures of speech to try to make a larger point about life. When he says, for instance, that he "thinks" he knows these woods, the word "thinks" suggests he doesn't really know them at all, for all that he passed them a thousand times. Of course, in a literal sense he knows them as a familiar landmark. The poem, however, is suggesting a different, deeper kind of knowing beyond the literal that only emerges when we take the time to stop and really see a scene we might have passed too many times to count.

"Downy flake" is a figure of speech. The flakes of snow falling are not literally made of down or soft bird feathers. They are made of frozen water. But by likening them to down, the narrator is trying to convey a sense of the dreamy beauty of the scene.

Likewise, in a literal sense, it is simply a waste of words to repeat the last line of the poem: "And miles to go before I sleep." Why would he do that? We have already heard the line. Repeating it, however, is a literary device. The poet doesn't have any reason to do this, except that he is trying to communicate a deeper truth. He repeats the lines, perhaps to indicate how very unwilling he is to leave a beautiful scene. He also repeats the line to emphasize, perhaps, that life's most important moments are found in the spaces between more "important" tasks. 

"Stopping by Woods on a Snowy Evening" is remarkably free of figurative language; most of the poem is stated factually, without metaphor or allegory. The narrator thinks he knows the owner of the woods, who lives in the village. The woods are "filling up with snow." The lake is frozen, the evening is dark, and the woods are "lovely... and deep."

While there are others, the obvious example of figurative language is seen in the narrator's personification of his horse, which seems puzzled by the narrator's decision to stop and look at the woods instead of continuing on the path.

My little horse must think it queer
To stop without a farmhouse near
[...]
He gives his harness bells a shake
To ask if there is some mistake.
(Frost, "Stopping by Woods on a Snowy Evening," eNotes eText)

Of course, horses don't think abstractly enough to consider things "queer" or strange, and they cannot ask any specific question. Instead, the horse is simply accustomed to moving along the path, and is waiting for instruction; it could be shaking its bells to shake snow off its neck. The narrator, however, is feeling doubt about his course in life, and so humanizes the horse, projecting some of his doubt into otherwise instinctual actions.

There are figures of speech in Frost's poem, "Stopping By Woods On A Snowy Evening." The narrator states that he has promises to keep and miles to go before he sleeps.

Some critics think that the narrator is comtemplating suicide. Who else wood stop by woods on the darkest evening of the year to watch woods fill up with snow?

Even the little horse thinks it is strange to stop between the woods and frozen lake on the darkest evening of the year.

The last lines could be symbolic meaning a long life up ahead. Miles to go before I sleep could be a metaphor meaning the narrator has many years to go in life. Since he has made promises, he must carry on in life and not give up just yet:

The woods are lovely, dark and deep.    But I have promises to keep,    And miles to go before I sleep,    And miles to go before I sleep.

Let's go back and look at that "easy wind and downy flake" business. Is the wind actually "easy," by technical defintion? Or is Frost using figurative language here to make the reader sense that the wind is not harsh or bitter, but rather a gentle and light sensation? One could argue that both "easy wind" and "downy flake" utilize figurative language, in that neither description is completely literal. Downy is an adjective which most accurately described light feathers, such as goose down. However, snow is not feathers, and therefore, this description could be seen as figurative.  

The short answer to your question is no, in the sense that the poem contains no metaphors, similes or rhetorical flourishes. Frost narrates his experience in very simple language - most of the words are monosyllables - and direct narrative. Even his use of adjectives is sparing in what is a very visual poem: the words 'lovely, dark and deep' are used of the woods, the lake is 'frozen', it is the 'darkest evening of the year', and there is a 'sweep of easy wind and downy flake' (these two the nearest to metaphor in the poem), but beyond this Frost leaves it to the reader to create the scene. I don't think the horse is is meant to be in any way figurative either: a horse used to travelling this route without stopping might well be puzzled by this pause, especially at the end of what has perhaps been a hard day's work.

However, that is to tell only half the story. The poem as a whole is seen as figurative, even symbolic, by many readers. We have to ask ourselves what this journey might represent beyond its literal sense. Is it a journey of life, a life in which we all too often have to curb our natural impulses and desires because of the pressures and 'rules' that govern us? Is the poem saying something important about decision-making, ethical dilemmas, beauty, duty, impulse? In other words, is the poem about abstract and philosophical issues despite its simple language describing concrete experience?

There are no similes in Frost's poem, but there are a number of literary devices the poet employs to create a tone of physical and emotional isolation, both states the speaker does not find particularly uncomfortable.

For example, Frost turns the traditional expectations of "dark" and "cold" into spaces which are more welcoming than alarming. While "the darkest evening of the year" might mean foreboding in another poem, here it implies a state in which the speaker feels at ease, cloaked in darkness and able to observe the woods at his leisure, without anyone asking him what he is doing or why he is doing it. The evening, rather than being cold and unpleasant, is described as being enveloped in "easy wind" and "downy flake." The speaker also calls the woods "lovely."

As for figurative language, the speaker's horse is subjected to some mild personification, when the animal is depicted as thinking it "queer / To stop without a farmhouse near."

Figurative language is also employed in the twice repeated final lines, "And miles to go before I sleep." While on the one hand, it may simply mean that the speaker must continue on a great distance before finding a bed, it may also figuratively mean that he has a long life ahead of him before "eternal rest" draws nigh.

A simile is a comparison that normally uses "like" or "as"; however, this poem has no similes.  One of the literary devices that is not figurative language that is used that is obvious is repetition.  It is used in the last 2 lines of the poem, which is very important.  Repetition is used for emphasis; therefore, Frost must have felt the last 2 lines to be very important since they are identical.  More than likely, Frost was having his narrator repeat the last 2 lines because the narrator realizes he must now return to the "real world."  He has had his moment of connecting to nature; however, his horse has shaken his harness bells and is reminding the narrator that they have a long way to go before they get to their destination.

There are a couple of instances of alliteration, in line 4 and line 11.  Alliteration is the repetition of consonant sounds at the beginning of 2 or more words.

The first thing to notice is the meter of the poem. Frost uses iambic tetrameter (four repetitions of an "unstressed-stressed" pattern), which seems to recreate the sound of a horse's hoofbeats. It's a pleasant sound that lulls the reader and could make him feel part of the scene. The poem is filled with imagery that helps set a peaceful atmosphere and tone. Through Frost's words, one can visualize snow falling lightly in the woods while a solitary rider and his horse are the only witnesses. The use of alliteration in the first stanza ("w", "wh", "h") creates soft sounds, much like the evening wind blowing thorugh the trees. Assonance ("o" and "ah" sounds) creates a similar effect. Frost uses a hyperbole when the narrator says that he will "watch his woods fill up with snow", and that aids the imagery. In the second stanza, the horse is personified and acts as a witness with the rider to the peaceful scene. The rider is jarred back to reality by the fourth stanza with the line "But I have promises to keep"; however, the use of repetition in the lines "and miles to go before I sleep" almost makes it seem as if the rider is reluctant to leave and is trying to convince himself that he must be on his way.