There aren't any magical princes here or dwarfs, but the imagery of the girl's snow-white extremities may make us think of fairytales nonetheless. Usually writers use this sort of description to give us a sense of innocence or youth. The same thing is probably happening in Yeats's poem, too.
Lines 3-4: We first see the girl with "little snow-white feet." The tiny size and pure color give us the sense of innocence and youth as she tries to teach the speaker about love and life.
Lines 11-12: Later we see her with a "snow-white hand" that she lays on the speaker's shoulder as an extra form of persuasion. But with or without that hand, the speaker isn't listening.