Some of the saddest songs I would have to hear in Zelda would be titles like
Midna Says Goodbye. It's the combo of the cinematic and how the chorale is written that makes it seem sad.
I agree with Y2K3 that the Final Hour is sad. However, if you listen to the song with an open mind and think about the game, the song is not only saddness. You have the eerie tone in the background that makes the song seem not only sad, but scary and full of anxiety as well, as would all of the people in Termina would feel. They would be sad and scared to die, and it is the song that fully expresses that feeling as well. I don't think that Midna's Lament was that sad...in fact, it got annoyingly repetitive at times during that scene.
Song of Healing can be sad as well, because it is mainly played to people who have died or are dealing with a hard time. However, the song, with the piano part, makes the song feel optimistic at the same time. I suppose the Song of Healing can, at the same time, be a song of hope for a better life/afterlife. I suppose this can be said the same for
Farewell King of Hyrule in Wind Waker and
Saying Goodbye in Spirit Tracks.
I suppose some other songs that could be slightly depressing are the awakening of the sages in Wind Waker. Koji Kondo is a serious beast when it comes to writing, and can make any Zelda moment feel alive. Happiness, sadness, he can make you feel it all. Sorry for the off topic ending, but it had to be said. So, I suppose I don't have a most sad Zelda song, but perhaps a small list of the saddest tunes in Zelda.