Most of the conflicts in Truman Capote's 1945 short story are internal; they take place in the mind of Miriam Miller. It is arguable that the intense loneliness she suffers after her husband's death leads her to slowly lose touch with reality and gives rise to full-blown delusion.
The precocious child with the silver white hair seems to materialize from the hushed and snow-covered city. She is likely a projection of Mrs. Miller's deteriorating psyche. Miriam Miller is elderly, and Miriam is a child. Mrs. Miller is kindly and retiring while the child is cold and demanding. Mrs. Miller dresses plainly and lives humbly, but Miriam dresses extravagantly and has an appetite for delicacies and French porcelain dolls. Miriam dictates her desires while Mrs. Miller accepts what she gets. Only through the presence of Miriam do Mrs. Miller's internal conflicts become in any way "externalized," but all the same, they are not witnessed by anyone outside her apartment.
The external conflict materializes when Mrs. Miller's delusion becomes too powerful, and she seeks help from her neighbors. The man's investigation of Mrs. Miller's apartment proves that the child does not physically exist, and Mrs. Miller's delusions conflict with the reality of her situation. The conflict is left unresolved when the unwelcome manifestation of her mental illness intrudes once more.