Final answer:
The original question appears to refer to a scene from 'A Charlie Brown Christmas,' but the provided excerpts do not contain the information needed to answer what song Schroeder played for the Christmas play. Therefore, an accurate answer cannot be given based on the context given.
Step-by-step explanation:
The question refers to a scene where a character, Schroeder, is expected to play music for a Christmas play. The textual excerpts provided do not directly mention Schroeder or a specific Christmas play, so they do not give us the answer to what song Schroeder played. Instead, the excerpts describe different scenes involving music: the first from F. Scott Fitzgerald's work where music brings nostalgia to the character Dexter, the second from Henrik Ibsen's play 'A Doll's House' where Helmer plays the piano for Nora to dance, and the third describes the admiration for a trombone rendition of 'Home, Sweet Home.'
Given the context, it seems like the original question might be referencing 'A Charlie Brown Christmas,' where the character Schroeder plays a piano piece for the Christmas play. However, to provide an accurate response, we need correspondence directly tied to that specific work. Without the correct reference, it is not possible to answer the question definitively.