Before someone complains, I’d like to say that I based this mostly on their personalities, not just in their powers/abilities. If you don’t agree with me, no need to be rude, you can gently say what you think. Also, my English is not perfect. You can correct me if you see any mistakes.
Jack Frost – Jack is a son of Hermes (God of Roads and Merchants). Jack is always playing tricks and having fun. He kinda makes me remember of Hermes and his children.
After Jack’s death, his sister joined the huntresses of Artemis. She was really young at the time, but a really good fighter. To honor the memory of her brother, she was always telling stories to the hunters about a guy named Jack Frost, the one that brings the fun to Snow Days.
When she told Artemis about her brother the goddess was so amazed with the stories that she made Jack came back to life. (Artemis is also the goddess of the moon. And this makes the “man in the moon” a woman in the headcanon.
Gods, I’m genderbending the moon!)
With time, Jack found out he had cool ice powers and that he could fly. But he had to carry a curse: he could only be seen when people believed on him and the stories that once were told by his sister, who died on battle years later.
Rapunzel – Rapunzel is totally a daughter of Apollo. She loves to sing (Apollo is the god of music), she has a hair that can heal people (god of healing), and he is also the god of the sun and light.
Rapunzel was kidnapped when she was just a baby by a vain woman that thought she could be prettier than Aphrodite. And you don’t mess with the gods! Aphrodite said to Apollo he should cut Rapunzel’s hair and end with its magic before something bad could happen. But there was a prophecy that said only a son of Hermes could end with that power.
Rapunzel knew Jack’s stories from books she read, and one day she saw him. They became friends. Rapunzel used to think he was the son of Hermes of the prophecy, but it turned out to be Flynn Rider.
Hiccup – This guy is a son of Hephaestus (God of Fire and the Forge). Stoick himself is Hephaestus, but at the time he was tired of the Olympus drama. Then he created Berk, where he could build a family in there for a while.
Hiccup has amazing mechanical abilities, but he is not as strong as the rest of the Isle of Berk. He isolates himself, not only because he thinks he is weak, but because he can control fire. And this ability, for a demigod, is very dangerous. But when Hiccup finds Toothless, he discovers he can use the power to bond with dragons.
Merida – Daughter of Zeus (Lord of the Sky). Merida is tough and headstrong. And even if she doesn’t like to admit, she has the spirit of a leader. She doesn’t change her mind very easily, and this sounds like a daughter of Zeus to me.
After turning her mother into a woman again, Merida realized she wanted adventures. She joined the huntresses of Artemis, and it was there she first heard of Jack Frost, which was a very popular tale between the huntresses.
One day she was visiting Berk, a place where dragons were allowed everywhere and the snow looked magical, Merida were amazed. She wanted to live in there forever. She met a guy named Hiccup, who showed her all the beautiful places of that land.
A prophecy brings the Big Four together. They have to fight Pitch, a son of Phobos that holds a lot of grudges because of the gods and wants the Olympus down. Only Jack, Rapunzel, Hiccup and Merida can defeat him, but four is a really unlucky number for a prophecy.