Ehhhhhh. Writer here. This is a really short prologue to the story. Please enjoy.

For Katsuki Bakuguo, winter was like a disease. He dreaded the cold, and even if he could manage to keep himself warm because of his fire based quirk, he still hated the sight of snow. Ever since he was a small child, before he developed a quirk, he had hated it. It was mostly because the cold was nothing but a parasite in his eyes; leaching the warmth out of anything and everything it came into contact with.

He was in the snow now, wearing a pair of winter boots that were barely held together by the cheap stitches that lined it and a light blue coat with faux fur lining the inside. His cheeks, still chubby with baby fat, were rubbed raw and red from the bitterly cold air while his small childlike hands were wrapped into fists with sparks of red fire springing from the uncovered skin every once in a while for warmth. It was a school day, but the roads had iced over so badly that Katsuki's mother had allowed him to stay home.
The sky was clear of clouds, and the sun shone down with a clear brilliance, but despite that, it only seemed to make the temperature seem colder. Tilting his head back to stare at it with narrowed eyes, Katsuki lifted his hand to the sky and made a fist. The sun was up there, but it's warmth was unattainable, hidden behind a blanket of cold. It briefly reminded him of a god sitting atop the heavens, looking down on the world with a cruel justice.

He shivered. "It's cold..."
The crack of ice made him whip his head to the left. The temperature seemed to drop even more, if that was even possible, and Katsuki felt his eyes widen against his will as he looked at the figure in front of him. The first thing he noticed was that it was a girl, and an exceptionally pretty one too, but that was overshadowed by the fact that she wasn't wearing anything except a plain white dress that reached her knees. Her hair was long, and trailed down her back in curling tendrils of silver, while her dark blue eyes were fixated on Katsuki's feet, wide and curious.
Katsuki stared at her, his mouth slightly agape. Her gaze unnerved him, and for a brief moment of panic, he laugh she would say something about the deplorable state of his winter boots. "Hey," he said with a scowl twitching onto his face. "What are you looking at?"

It came out ruder than he intended, and he resisted the urge to flinch at his acerbic tone. To his surprise, the girl didn't answer and instead pointed at his feet. Katsuki growled in his throat, ready to throw away any kind of civility he possessed and snap at her, but just as he was getting ready to yell, she spoke up.
Her voice was alarmingly soft and held an air of faint wonder to it, and Katsuki had to strain his ears to hear her. "The snow is melted."

Katsuki looked down, and to his surprise, the girl was right. The snow at the base of his feet had melted into a puddle of lukewarm water, and was now soaking into the fabric of his boots. He let loose a yell of alarm and jumped back, creating a path in the snow with his heat. The girl's eyes watched his movement for a moment, then went back to the puddle. A crease formed in her brow as she took a step forward, and Katsuki saw that her feet, which had previously been hidden by a flurry of snow she was standing in, were bare. The most amazing thing was, she didn't even seem bothered by it.
As Katsuki watched with muted amazement, the girl reached down and placed her fingertip on the surface of the water, and it froze over almost instantly. The girl's expression softened into a placid look. "Fixed it," she said.
"Aren't you cold?" Katsuki asked harshly, his voice painfully loud and harsh compared to the soft ringing of her's. The girl looked up, surprised at how angry he sounded.
"No," she replied in her monotone voice. "Are you?"
Katsuki opened his mouth to answer, but he was cut off by an icy hand wrapping around the base of his wrist, right where the warm refuge of his coat sleeve ended. He flinched, choking on his words in shock as he attempted to pull away. The girl looked confused as she experimented with her grip, testing different strengths. Katsuki ripped his hand away, unable to bear the pain anymore.
"You're warmer than the others." She said simply. "The others freeze when I touch them."
"What the hell!" Katsuki yelled angrily, tugging down his coat sleeve to cover his damaged flesh, which was cracked and bleeding. A few drops dripped to the ground and hit the snow, burning right down through the white blanket until it hit the ground. The girl's eyes widened with a mixture of fascination and curiosity. His quirk flared up on it's own, sparking an angry flame in the palm of his hand."You're like ice!"
"I know." She said it casually, as if she were used to people commenting on it. Feeling a bit guilty, Katsuki sighed and looked her over. She couldn't have been any older than ten, which made them about the same age.
"Is that...your quirk, then?" He asked, a little unsure of himself. The girl shakes her head, looking down at her hands. Katsuki hadn't noticed it before because of how pale her skin was, but there was ice forming at the edges of her fingertips.
"This isn't my quirk, I'm just colder than other people." She said stoically. "But Daddy says I'm not supposed to use my quirk. He says it's too dangerous."
Katsuki frowned. "Quirks are meant to save people. How is your's dangerous?"
The girl paused, lifting her eyes slowly to meet his. There was a silent battle in them, and for a moment, Katsuki saw a blizzard reflected in them. A spike of fear rolled up his spine that was colder than the air around him.
"My quirk is meant to kill people," she said, her voice louder than before. "It killed Mommy."