Robert Frost is one of the greatest modern poets of American literature. His poems are embedded with thought-provoking symbolism. In the poem "Desert Places," Frost delves into the theme of loneliness and disconsolateness. He uses words such as "falling," "loneliness," "snow," and "absent-spirited" to reinforce the idea of isolation and create vivid imagery of desolation.

The title "Desert Places" has a literal meaning referring to barren places in the environment and a connotative meaning referring to the spiritual wilderness. In the line "They cannot scare me with their empty spaces," the word "they" has multiple meanings and several interpretations. It could refer to scientists or nature in its various forms. In the last stanza, the speaker declares that he is not scared of physical emptiness but of spiritual barrenness.

Throughout the poem, Robert Frost depicts the loneliness and isolation he feels staring at a dark empty field as snow descends onto it at night. He has an overwhelming sense of separation from nature, animals, and other humans as he contemplates his own loneliness. In the fourth stanza, Frost writes, "They cannot scare me with their empty spaces." Frost then proceeds to comment on the distances between stars in outer space where human life does not exist. In my opinion, "They" refers to the scientists who describe the vast emptiness of space which makes individuals feel inadequate as we gaze into the limitless sky. Frost comments that even the scientists cannot scare him with their discussions of the infinite distances in space when compared to his own "desert places." The "desert places" Frost is referring to are in his own mind, spirit, and psyche. Frost is more afraid of the workings of his own imagination which give him the most haunting feelings of loneliness that nothing can compare to. 

1. I believe that "they" in this line does not refer to anyone specific.  The theme of the poem is how the speaker feels alienated from everything around him.  So I think he uses the word "they" to emphasize that he feels like it is him against everything else -- that there are forces that are against him.
2. These are the empty and lonely spaces in his own psyche.  They are the parts of him that are not content, which feel melancholy and perhaps even despair.  This emphasizes that his problems are within himself.