Which figures of speech are in the poem "Stopping by Woods on a Snowy Evening" by Robert Frost?

This poem uses imagery, language that conveys sensory information, in order to help us understand how solitary the speaker is, and how dark and beautiful the woods are.  The second stanza is most concerned with visual imagery: things we can see. There is no "farmhouse near" and the speaker has stopped to rest "Between the woods and frozen lake" on this, the "darkest evening of the year." It is easy for us to visualize his location with the help of these images. The third stanza is most concerned with auditory imagery: things we can hear. We can imagine the sound when the horse "gives his harness bells a shake" as well as the near-silence of soft-blowing breeze in "the sweep of easy wind and downy flake." The words, "downy flake," work as a visual image too: we can imagine the kind of snow that is fluffy and drifts slowly to the ground.
Some readers also interpret "sleep" as a metaphor for death in the final two lines which repeat, "And miles to go before I sleep." In this reading, the speaker's solitary journey through the woods—the "miles" he goes—becomes a metaphor for life, for all the work we must do before we can go to our final rest, so to speak.
In addition, I agree with the other commenter who discussed the light personification of the horse in the second and third stanza. To attribute the abilities to "think it queer" to stop in such a solitary spot and to shake his harness bells "to ask if there is some mistake" qualifies as personification, which is when the poet gives human characteristics or abilities to something nonhuman.

As many scholars and readers have noted, Robert Frost's "Stopping by Woods on a Snowy Evening" has a decidedly small amount of figurative language. Indeed, the poem is direct and concise, as though the poet wanted to trim down any unnecessary baggage. There are, however, a few instances of figurative language (or, as you say, figures of speech). For example, Frost says "My little horse must think it queer / To stop without a farmhouse near" (5-6), and this line actually contains some very subtle personification. The horse might be acting perturbed by his rider's unexpected change in routine, but he certainly isn't actually mulling the event over in his mind like a human being, or thinking it "queer." In that case, Frost actually uses some slight personification by framing the horse's actions with subtly human characteristics.  
Don't let the brevity of this poem fool you: the piece may be concise, but it communicates a vast array of meaning, much of which has been hotly contested by critics. As such, though "Woods" doesn't employ many examples of figurative language, it's still much more complex than it at first appears. As such, it's well worth reading and analyzing closely.