Euron Greyjoy could be a great base. He's already a fearsome and somewhat unhinged character. In a fanfiction, you could expand on his ambitions. Maybe he has a grander plan than just ruling the Iron Islands. He could be secretly in league with some powerful sorcerers in Essos, using their magic to enhance his fleet and gain an advantage over his enemies in Westeros.
The Mountain, Ser Gregor Clegane, could also be a starting point. In a fanfiction, instead of just being a brute for hire, he could be a more complex warlord. Maybe he has his own territory in the Westerlands that he rules with an iron fist. He could be involved in a power struggle with other lords, and his size and strength are just part of his arsenal. He could also have a secret family that he's trying to protect while maintaining his fearsome reputation.
Arya Stark would be a great choice. You could write about her using her assassin skills to target key military leaders during the war. For example, she could infiltrate enemy camps disguised as someone else and take out important commanders, which would have a huge impact on the battles.
Arya Stark could be an interesting choice. Imagine if someone else transmigrated into her body. They would have to deal with her complex relationships, like her hatred for the Lannisters and her training with the Faceless Men. It would be a challenge to continue her story while also bringing in new elements from the transmigrator's personality or knowledge.
Definitely Tyrion Lannister. In a crossover with 'The Simpsons', he could bring his sharp wit and political acumen to Springfield. He'd probably outwit Mr. Burns in no time. His complex personality and ability to adapt would make for a very engaging character in such a crossover fanfiction.
It could be Jon Snow. If he has a Stand in the fanfiction, combined with his already proven leadership skills and combat abilities, he would be a force to be reckoned with. His ability to come back from the dead might also be related to his Stand powers in some way, making him even more formidable.
Arya Stark would be a great choice. She's already a skilled fighter in the ways of the Faceless Men. Training with samurai could enhance her skills even further. Her journey of self - discovery could be influenced by samurai teachings about honor and discipline.
Clark Kent and Arya Stark would be an interesting pairing. Clark with his superpowers and noble nature, and Arya with her assassin skills and strong will. They could learn a lot from each other. Clark could teach Arya about using her powers (if she were to gain some in this fanfic) for good, and Arya could teach Clark some of her stealth and combat techniques.
Reincarnating as Tyrion Lannister would be really interesting. He's already a complex character with a sharp mind. As someone reincarnated, you could use your modern ideas to enhance his political acumen even more. You could also try to change his relationship with his family for the better, or at least make his life less miserable while still being the clever dwarf everyone fears and respects in the political arena.
Jon Snow would be an interesting character to be an avatar. Given his complex backstory and his role in the fight against the White Walkers, as an avatar he could gain even more powerful abilities. Maybe he could have the power to control the elements, which would be a huge advantage in battles. He could use this to create blizzards against the White Walkers or to put out fires during the sack of King's Landing.
Black Widow. She's a master spy and assassin. In the world of Game of Thrones, she could easily blend in with the various spies and informants. She could play the game of thrones better than most of the characters there, using her charm and combat skills to manipulate the situation to her advantage. She might even be able to uncover some of the deepest secrets of the Seven Kingdoms.
Jon Snow would also be a great addition. His journey from being a bastard to a leader in Game of Thrones could be paralleled in the world of Frozen. He could learn from Elsa about controlling his powers (if we assume he has some new ice - related powers in this crossover) and in turn, teach the people of Arendelle about loyalty and sacrifice, which are values he has held dear in Westeros.