"Desert Places" uses plenty of alliteration, often to reinforce the imagery it's describing or to highlight important words and ideas.
Lines 1-2, for example, contain a number of emphatic /f/ words, which help create a driving, slightly uneven rhythm:
Snow falling and night falling fast, oh, fast
In a field I looked into going past,
The thick, chaotic swirl of /f/ sounds might be compared to the thick, swirling snowfall. In the same stanza, the soft, repeated /s/ sounds of "smooth in snow" seem to make the phrase itself run more smoothly.
In the third stanza, alliteration links a number of thematically meaningful words. Consider the /l/ words "lonely," "loneliness," "lonely," and "less" (lines 9-10); the /b/ words "blanker" and "benighted" (line 11); and the /n/ words "no" and "nothing" (line 12): not the world's most cheerful group! These words have to do with isolation, diminishment, darkness, and nothingness: key themes in a poem that's all about inner as well as outer desolation. Again, alliteration also simply makes the language flow smoothly, subtly mirroring the smooth blanket of snow being described.
Finally, a run of /s/ words appears in lines 13-14: "scare," "spaces," "stars," "stars." This sibilance sounds a bit eerie, like whispering or hissing—an appropriate effect for lines about vast, chilling emptiness.