Well, it could be really interesting. Harry Potter characters have magic, while in the Iron Throne world, it's more about political intrigue and battles. Maybe Harry could use his magic to solve some of the power struggles in Westeros. For example, he could use the Patronus charm to drive away the White Walkers if they ever showed up in this fanfiction mash - up. And Hermione would probably be fascinated by all the different cultures and histories in the Seven Kingdoms and start researching them right away.
If the Harry Potter characters were in the Iron Throne world, there would be a huge clash of values. The wizarding world has a certain code of ethics regarding magic use. In Westeros, power is often seized by any means necessary. Ron might be a bit out of his depth at first, but he could probably make some good friends among the knights. The Hogwarts students would be shocked by the violence and backstabbing in the Iron Throne world. They might try to introduce some of their own laws and values, which would surely cause a stir among the lords and ladies.