In "Stopping by Woods on a Snowy Evening" by American poet Robert Frost, the importance of using the pronoun "I" is that this gives an intimate, personal touch to the poem. The reader can better understand the mindset and deep inner thoughts of the poet through the use of this pronoun.
If Robert Frost had constructed the poem so that it read like a general commentary of what any person thinks while in this winter environment then the poem would not pack as much punch so to speak. It's when a writer of a poem, or a novel, short story, a creative non-fiction piece, or an essay, personalizes it that a reader is drawn into the story more.
The use of the "I" pronoun lets the reader identify with the author and what he or she is experiencing. It is as if the poet is inviting the reader into sharing a personal confidence or even in some cases a secret. This helps the reader identify with the unique, individual writer and his or her views on life.
Consider the very first line of the poem:
Whose woods these are I think I know.
Immediately the reader can see that the poet is in his own community and that he is familiar with the people and the land. He knows who owns what properties, and probably knows much more about the inhabitants of the community. Therefore, the reader is drawn into this time and place through the intimate knowledge of the area and its peoples by the poet.
In the final stanza of the poem, the reader learns more about the poet himself through the use of the pronoun “I.” Here, we have a deeper revelation of the man, what he is thinking concerning his life, not just his views on his neighbors and the community at large. This is evident in these lines:
But I have promises to keep,
And miles to go before I sleep,
The use of “I” lets the reader know more about the poet as an individual. The reader understands that the poet has promises to keep, which prompts the question, “What are these promises?”
Furthermore, the next line, which is subsequently repeated, lets the reader know two things about the man: he has a long journey ahead of him both in real travel time, as well as in a life to be lived before he dies. The power of the poem is in the way Robert Frost personalized the poem with the use of the pronoun “I.”