In a fanfiction where Percy Jackson goes to Arendelle, there are so many possibilities. He could make friends with Kristoff, who would be really curious about Percy's adventures. Percy might also discover that there are some hidden connections between the magic in Arendelle and the powers related to the Greek gods. For example, the ice magic could be related to some ancient and forgotten god in the Greek pantheon. And when it comes to the trolls in Arendelle, Percy could either be scared of them or find a way to communicate and cooperate with them to protect Arendelle from danger.
Well, he might meet Elsa and be really amazed by her ice powers. Since Percy is used to dealing with all kinds of magic in his own world, he could either help Elsa control her powers better or get into some trouble because of the different nature of the magic in Arendelle. Maybe he'd also team up with Anna to fight against some new threat that emerges in Arendelle.