Percy is battling the titan atlas in the titan's curse when his injuries become too great. Athena decides that to thank him for saving her life she will turn him into a (minor) god and therefore save his life. The prices for this are memory loss and not being seen. He turns into Jack Frost but Kronos, the titan of time, transports him back in time to Arendelle. He can't be seen by anyone except the trolls but he decides he won't live with them. Meanwhile Elsa is suffering because her parents "died" when really they, Boreas and unspecified mother (probably a one night stand with Aphrodite, anna with another mother), left due to the rule about godly parents and their kids. Elsa eventually turns into Khione and Percy stays awesome.
It could go anywhere from here. I just thought it fit well with the plots from both movies. Jack Frost is made from the moon and Elsa has ice powers. I don't care what characters are included or which plots are used I just thought it was a great outline for a story. Also Elsa/Khoine wouldn't want to help the demigods in the lost hero when they go to Boreas because both her and Piper are daughters of Aphrodite but only Piper got claimed. It also explains why Zues hates sons of Posiedon so much, on of them got to control weather which is Zues's domain. I also want to read this story so message me or something when you start the story.