Frostbite
Princess Elsa is 18 years old, it's 1839 her parents just died, and she is broken, she needs to know how to control these powers. She had been doing some research on places or people that can help her control it, and before her parents died, they had found some information on a foreign school called Hogwarts located in a land called England.
She sent one of the kingdoms ravens off with a letter to this 'school' to see if they would come to pay a visit, to try and help her at least. In three years she would be coronated a Queen if she could not control it by then, how could she ever rule.
It was Christmas before she heard back from the school, or three months to be exact. She was currently making gingerbread houses when a tall man appeared in the room.
"Who are you? GUARDS! How did you do that?" Asked Elsa, as the guards stormed in
"I'm Headmaster Black, you must be Elsa, please I got your letter" Replied the man
"Guards you may leave, Headmaster, sorry about that, I'm a princess, intrusions mean people want to kill you usually, thank you for coming, I honestly I would never hear back from you. I need help, I can't control my powers, I don't know what to do" Cried Elsa
"It's alright dear, why don't you explain the situation to me," said Black
"Well, when I was a young girl, I had these icy powers, I can control Ice and Snow, we all had fun with it until one day I accidentally froze my sisters head, the trolls managed to fix it by removing all memories of magic. My parents tried to get me to control it, but they did not know how. They died a few months back, on their way to a foreign land, and now I'm the Heir to the throne, but I still can't control my magic, and it's just getting worse" a still crying Elsa
"Okay, it is worse than I imagined, and we need to get you some help to control your powers, you see, you are called an Elemental Witch, you can control an element, but you are a powerful witch in your own right. We don't usually get students coming to Hogwarts going into the first year at the age of 18, however, we can make an exception, give you your own quarters, and you would not have to be sorted into a house, as a dignitary, you would be welcomed to eat at the Head Table. Please let us give you help" Replied Headmaster Black
And so, Headmaster Phineas Nigellus Black and Princess Elsa, went around the castle gathering everything she needed for her trip away, she said goodbye to her sister, and placed her in charge, should anything happen to her. Without further ado, they disappeared, disappeared to a wondrous place, a place teething with magic, this place was called Hogwarts, it was a castle, a bit darker than the one she owned, but a castle all the same, inside, however, was beautiful and stunning. Headmaster Black showed her to her private quarters and told her to settle in, he would be back in a few hours to get her, so she could eat and then they would go get some supplies for her, including her very own wand
You see, without being around Christmas, the school was not in session, there were only a few students around. Headmaster Black came and got her and took her to the Great Hall, where she was astounded by the wondrous room, the amazing tree, the spectacular sights on the ceiling. Headmaster Black had arranged with each of the professors to catch her up on the first-year training, thankfully there were not many magic lessons to catch up on. They would start in a few days, and by the new year, she should be all caught up in time to carry on with the tuition. Headmaster Black would be taking care of her Elemental training himself, this includes Occlumency because part of getting control of the powers means getting control of one's mind.
Once they had finished eating a wide array of foods, Headmaster Black took them directly to Diagon Alley, their first stop was Gringotts Bank, He told her that her magic would have likely come from a magical family, and she might have some money in vaults, if not her tuition would happily come out of the Hogwarts Account, including anything she may need.
The goblins ran the inheritance test on her, and did not find any vaults she was entitled to which perplexed the Headmaster, they did, however, offer a currency exchange for the Arrendelle Snowflake, they apparently did a lot of business over there. They offered to open a new high-security vault for her, as she was an incredibly important royal dignitary. She graciously accepted and got more Galleons than she thought she would. 1000 Arrendelle Snowflakes converts to 100,000 Galleons for a strange reason. With this money, she asked for the tuition for 7 years to be transferred straight to the Hogwarts vaults alongside a withdrawal of 10,000 Galleons for supplies she may need now and throughout the year.
Off they went down the alley, in and out of the shops, buying robes, books, potion supplies. She even managed to find a cute snowy cat in the pet store which she named Olaf. The destination was to Ollivander's to get his wand. Inside was a middle-aged man who the Headmaster called Gervaise. Gervaise was incredibly kind, if mysterious. They went through a tonne of wands with Elsa, before they landed on the perfect one, it was 7 and ½ inch Applewood wand with a drop of Unicorn Blood, freely given, and a hair from an Ice Phoenix. As soon as she touched this wand, she suddenly all the magic rushing through her, she could feel her power, she felt more control now than ever before. She waved the wand and froze all the shops on the street making it snow.
A/N: Did a fair bit of research for this, I'm looking forward to writing this further, it's quite interesting