Stormbreaker itself could be considered a character in a sense. If it were to appear in the Game of Thrones world, it would be an object of great power. Many characters would vie for it. It could end up in the hands of someone like Daenerys, who already has a connection to powerful and magical things. This would make her even more of a dominant force in the story.
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.
Arya Stark in a 'Naruto Game of Thrones crossover fanfiction' would be fascinating. If she were to learn some of Naruto's ninja skills, she would become an even deadlier assassin. And Naruto's influence might change her path a bit, making her less vengeful and more about bringing real change to Westeros.
Another interesting pairing would be AOC and Arya Stark. Arya is a fierce and independent fighter. AOC could inspire Arya to think about the bigger picture in terms of changing the social order. Meanwhile, Arya could protect AOC from the many enemies she would surely make in the cut - throat world of Game of Thrones as she tries to implement her ideas.
Arya Stark and Rebekah Mikaelson. Arya is a trained assassin, and Rebekah is a fierce vampire. They could learn a lot from each other. Arya could teach Rebekah some of her stealth and combat skills without the use of vampire powers, and Rebekah could introduce Arya to the world of the supernatural and its different rules of survival.
I think Daenerys Targaryen would be really interesting. If she were reincarnated, she could use her past experiences to be an even more powerful and just ruler. She already had a complex journey in the original series, and reincarnation would add more depth to her character. She might be able to avoid some of the mistakes she made in her first life, like trusting the wrong people.
One idea could be a character from the Stormbreaker universe somehow getting transported into the Game of Thrones world and having to navigate its political intrigue. For example, they might use their unique skills from Stormbreaker to gain an edge in the power struggles of Westeros.
I think Jon Snow and Spock would make an interesting pair. Jon is a natural leader, and Spock's logical thinking could complement his more instinct - based leadership. They could learn a lot from each other, with Jon showing Spock about the harsh realities of a feudal society and Spock teaching Jon about the power of reason.
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.
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.