In Majora's Mask, there are so many emotional moments, and a lot of them are bittersweet moments, being in someways "heartwarming" but in other ways sad and desperate. I should also point out that I have never 100%'d Majora's Mask, so I don't know every part of the game. However, there are so many moments that I'll just rattle off a few of my favorites.
I'm sure if I sat here all night I could think of dozens more, but those are the times in the game when I clearly got the sense of despair, and therefore to me those are the saddest/most heartwarming parts.
- when you speak to the Goron Elder as Darmani and he wants to go back to put his son to sleep, and to comfort him, but he can't, so he struggles to remember the Goron Lullaby
- when you speak to Darmani and he tells the story of being unable to help his people in a time of crisis
- when you heal Pamela's father and the two are reunited
- Anju and Kafei for reasons that are self explanatory
- obtaining the Kamaro Mask from the dying dancer
- the story of the Skull Kid
- Clock Town on Day 3. Every part of it, the sense of despair, the reactions of everyone
- for me, any time when you go back in time late on Day 3 as the earth is rumbling, it almost feels like you're going to an alternate timeline where the people on this timeline are going to die, and you're running away and escaping that fate. I'm not suggesting there actually is an alternate timeline, but it just gives that type of feeling to me.
I'm sure if I sat here all night I could think of dozens more, but those are the times in the game when I clearly got the sense of despair, and therefore to me those are the saddest/most heartwarming parts.