Tom Hillman has a wonderful meditation on The Passing of Arwen Evenstar at “Alas, not me”.

One tangential thought struck me at the end. Bilbo also wrote, “I sit beside the fire and think of how the world will be / When winter comes without a spring that I shall ever see.” Which didn’t come true — Bilbo passed over the Sea in the autumn.  But that couplet matches perfectly with Arwen’s death “when the mallorn-leaves were falling, but spring had not yet come”.

Arwen must have heard Bilbo sing that song. Using a good poem only once is not how Bilbo does things. Perhaps she was struck by the poignancy of that line, just as I was. Maybe Bilbo was one of the people from whom Arwen learned how to be mortal.