The narrator's mood when he begins the story 'The Summer of the Beautiful White Horse' can be described as nostalgic and reflective. The opening lines of the story indicate that the narrator looks back on his childhood with fondness and a sense of wonder, referring to it as a time when "the world was full of every imaginable kind of magnificence, and life was still a delightful and mysterious dream." This sets the tone for the story and invites the reader to share in the narrator's reminiscence of a memorable and cherished episode from his past.