Which, of course, you won't name....
I get this feeling you're one of those people who doesn't like to replay games that much.
I know I'm jumping into the conversation here, but I believe I can give you some of the details you desire. It's true that not every character is morbidly depressed on the outside, but almost all of them are on the inside. When you go into a public school, not everyone you meet is going to be crying, throwing a fit, or screaming, but many of them still suffer inside. This same realism is carried out in a thoughtful way in Majora's Mask. You could almost consider it an artistic style; how does a peaceful, happy population respond to terrible suffering and death?
As for the characters you wanted to know about:
Anju is disdained by her grandmother in spite of trying to be helpful, cries in one scene from missing her fiance, and, in one possible ending, blatantly ignores her mother's wishes to hide and waits for her fiance to return in the Stockpot Inn...as the moon is minutes away from destroying all life in Termina.
Deku Butler is implied to have a son that went missing and looks just like Link's Deku form. At the end of the game, he appears to have found his son in the woods, dead and locked in rigor mortis. Further speculation could lead us to believe Skull Kid murdered him and cast his appearance upon Link early in the game.
Kafei was cursed into child form days away from his wedding and will stop at nothing to break the curse and reunite with his fiancee Anju. His unfaltering seriousness and devotion to his lover are notable.
The Postman is comically loyal to his job...so much so that he is torn whether or not to flee Clock Town, even when the moon is crashing down upon him and he clutches his head in his hands behind the office.
Mutoh has essentially given up on life and initially tries to deny Termina's impending doom, then resigns himself to his fate and curses the moon as the last man standing in Clock Town.
Romani is a sweet, innocent little girl who just happens to have the capacity to wind up brain-damaged from an alien invasion, breaking her disbelieving older sister's heart.
Cremia inherited the ranch from her dead parents and, depending on your actions with Romani, either has to put up with greedy bandits trying to steal her cow's milk (as the world is close to ending, no less) or mourning Romani's alteration from alien experimentation.
Skull Kid is an unfortunate victim of the whole disaster. Starting as a lonely child who met two fairy friends, his mischief cost him dearly as he stole Majora's Mask and wound up under its evil influence. So not only is this a case of an innocent child being taken advantage of and forced to do things he'll regret, but the reason he's lonely in the first place is because he perceives the Four Giants as having abandoned him.
Mikau tried to prove his love and loyalty to a fellow band member by rescuing her kidnapped children (still in eggs), but wound up getting killed instead, his power transferred to Link after playing the Song of Healing.
The Moon Children appear in the most beautifully trippy area of the game and question your personal beliefs and convictions while asking you to give up the masks you've worked so hard for.
And really I could go on and on, but underneath the supposed happiness is clearly turmoil, depression, hate, angst, and sadness. Not to mention after making all that progress and helping all these people and getting to know them, failing to stop the moon means you're forced to watch as it utterly destroys your friends and progress. As I said once, Majora's Mask is a deep game because players prompt themselves to reconsider their beliefs and actions, not the game. If you can't see past the first layer, Majora's Mask loses much of its thought-provoking charm. Part of this charm actually comes from the distinction between the apparent lightheartedness on the surface and the deeper, darker issues underneath. If it was just one or the other, it wouldn't have been nearly as effective, but the contrast makes them both stand out.