Spoiler:
It's also symbolic of the struggle of a first-time playthrough of the game; when you get to that point of the game, you're typically beginning the Dawn of the Third Day; it becomes painfully obvious as to just what you are up against. Majora - a demon with powers beyond reckoning - and the Moon, slowly plummeting towards Termina. And what are you? A child, trapped in the body of a pathetic Deku Scrub. You don't have a sword, or a shield, or any gear, really; no, your only weapons are spit bubbles and Deku Nuts. Walking into that Observatory, listening to the music, observing the Skull Kid summon the Moon, and watching as the Moon sheds a single tear... knowing what you are up against, and knowing full-well that you don't stand a chance, the song, the scenery, and the events that take place in that Observatory are symbolic of a death march; knowing full well that you are hopeless, that everything is hopeless, but refusing to hang your head down and accept the depression of your inevitable death, however painful or certain it may be.
In other words, that song - that area, really - is symbolic of the loss of hope, and the bittersweet realization that defiantly living your last day with your head held up high is better than dying before you die. The whole area screams "bittersweet", and I feel like that was wholly intentional, considering the circumstances.
