The main character is Luna Lovegood and shows her life with Xenophilius. I am certain that I found this on FanFiction.net. Eventually, Harry and Luna develop a romance, and I specifically remember a moment where Luna and Harry bundle up together under a blanket. I also remember a moment where Luna goes swimming in the lake by Hogwarts and McGonagall yells at her because it is cold outside.
The Peculiar Life of Luna Lovegood
The story can be found here for anyone who is interested! I am so glad I was able to find this once more, because I didn't finish reading it, and now I can!