Putting these girls into a Hunger Games-style arena simply wouldn’t end with a Hunger Games-style brawl.
They’re all protagonists. They’re all strongly Good, philosophically and in practical terms.
Mulan is a soldier, so she’s capable of killing, but not murder. Merida can hold her own in battle, but won’t kill an innocent. Elsa could kill everyone, but she won’t. Many of the others—Snow White, Cinderella, Rapunzel—have primarily social strengths, as in charisma.
They wouldn’t fight each other. They would fight the Arena itself. And it’s likely that they would win. Why? Just think about their abilities, and then imagine the many ways those abilities could be used to break the Hunger Games.
Snow White: She’s an innocent, and probably the youngest. She’s the Rue of the group—so vulnerable that nobody can help but like her. Even small animals love her; in fact, she has the power to get small animals to do her chores for her. Never underestimate the power of a squirrel, bird, a badger in the right place.
Cinderella: Another innocent, and another girl with the power to communicate with animals. Her powers aren’t as extreme as Snow White’s, but she’s capable enough. She’s also an abuse survivor—which means she knows how to deal with trauma, because she’s done it before. And she has allies on the outside—a fairy godmother with transfiguration magic, who won’t be happy that her charge has been imprisoned in the Arena.
Aurora: She’s not much use in a fight, and she doesn’t have any particular powers (she’s animal-friendly, but not an actual animal-charmer the way Cinderella and Snow White are); but she’s kind and introverted, which means she won’t upset anybody. She’s also spent her entire childhood living in a cabin in the woods—she knows how to survive in the woods. With her around, they aren’t going to starve.
Ariel: She’s a specialist, the literal Aquaman of the group. In the water, she’s faster than anybody else, absolutely unbeatable, and she can talk to creatures that live in the water. As far as animal whisperers go, Ariel’s the only one who can actually talk in two-way abstract language with her animals friends, so that means that the group knows anything that’s happening anywhere near water once Ariel gets her fish spy network going. Unfortunately, out of the water, she’s very slow and probably has to be carried.
Belle: Is a nerd. That’s her strength and her weakness. She’s read every book she can get her hands on, and she has an inventor for a father. She’s got an extremely good brain in her head, and she’ll probably be the group’s source of information, though not their chief strategist.
Jasmine: Born and bred nobility, her primary power is her charisma and ability to communicate. Totally naive outside her native environment, she nevertheless has the wherewithal to think on her feet. She’s been on quite a few adventures with Aladdin, so she doesn’t scare easily. Jasmine won’t be a major asset, but she also won’t hold them back.
Pocahontas: It goes without saying that Pocahontas, along with Aurora, will be one of the group’s major food providers. Her biggest strength is her diplomatic ability; when the group threatens to fall apart when things get rough, she can keep them together. She has some minor animal-communication ability, but nowhere near some of the others’.
Mulan: The soldier. She’s a military girl, and she’s good at what she does. When someone needs to think fast, she can. She’s good at using the environment to her advantage, and she’s good at disguising herself and others. She’s likely to become their de facto leader. She can also train others in the basics of fighting, which is very useful because many of the other girls have no experience; while they won’t be fighting each other, the Arena itself is very dangerous.
Tiana: She hasn’t got any exciting powers, but she’s sure going to come in handy. She knows how to cook, naturally. She’s lived as a commoner for a lot of her life, which means she’s more independent than most of the other girls. She also has experience with magic, and has had to survive in extreme situations before (can you get more extreme than being turned into a frog?). She won’t crack, and she’ll be useful. Tiana will be just fine.
Rapunzel: If she’s still got her hair, she’s a serious asset. Rapunzel’s hair can heal anything, even old age. She can keep the entire group healthy. And the hair isn’t just a whole lot of dead weight, either; she uses it as an aid to do some pretty cool parkour-style moves. Rapunzel is also very strong, as shown by her ability to pull people up by her hair without breaking a sweat. If she hasn’t got her hair, she’s less of an asset, but her physical strength can still see her through (and quite possibly give Ariel a way to get around out of water). Don’t underestimate her charisma, either; if she can convince a bar full of ruffians to join her team, she can talk anybody into anything. Like Cinderella, Rapunzel has survived an abusive childhood. In her case, it was mainly psychological and emotional abuse, so she’ll be the one to see through the mind games the gamemakers try to play on the girls; she’s seen them all before from Mother Gothel.
Merida: Archery, obviously. She’s as good as Katniss, if not better, and she’s one of the few girls with the ability to attack at range. She can ride, survive in the wilderness, and keep her head in a crisis. No problems here.
Anna and Elsa: Have to be taken as a set. Each is willing to die for the other, and Elsa’s ice powers are prodigious. Anna and Elsa may be the main reason why the whole group is likely to try to defeat the Arena itself rather than fighting each other: Each sister knows she wants her sister to live, and each knows that her sister wants her to live. The only option for these two is defeating the Hunger Games together. Elsa has leadership experience, having been a queen; Anna may be younger, but she’s proven herself in crisis situations already.
There’s really only two ways this can end: The girls join together to fight the Arena, and win; or the girls join together to fight the Arena, and they lose. A win may still mean the deaths of several of the girls, and almost certainly at least one such death; but they’ll be deaths inflicted by the Arena itself. The first death will affect them deeply, of course; they may actually have to go through the entire ordeal with one or more of their number essentially disabled by emotional shock. But these girls have learned too much about the power of love, friendship, courage, and hope to give up in the Arena.
That says a lot about the Hunger Games, doesn’t it? A big part of the reason why the children in the Hunger Games kill each other is that they have lost hope. Their whole world says you can’t escape the Arena; their whole culture says you can’t defy the Gamemakers. There have been plenty of people as skilled as Katniss in the Arena, who didn’t manage to defy the games as she did, because they weren’t able to defy the basic concept of the Games: “You must kill each other. There is no other option.”
Ironically, I see a lot of Hunger Games fans looking at the Arena in the same way: A lot of people go in; only one leaves. They don’t challenge that; they focus on the strategy of survival. But as Katniss knows, and as the Disney princesses would understand, the other tributes were never the enemy.
Take a life lesson from this: When the power structure around you seems to be trying to pit you against other people, ask why. Challenge the paradigm. Chances are, the people you're being encouraged to fight aren't the enemy, and chances are, you'll be stronger together.