Krampus was once the leader of Santa's reindeer team, but was betrayed by them and turned into a monster.
Now he looks like a hybrid of a deer and a wolf.
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Backstory (sorry for my bad english ^^"):

Once upon a time, Krampus grew incredibly beautiful silver horns, which, unlike the others, he never dropped. He was very proud of them and with age only became more conceited, reveling in his uniqueness. Everyone who wanted to see his horns had to bring him some gift, give his thing or perform a humiliating task. Over time, his horns turned into a trinket shop, so many things were hung on them that he even walked slightly swaying under their weight.
Soon, the forest dwellers got tired of his arrogance and they stopped contacting him, so the deer remained alone for many years.

One day, he comes across an old man's house, who made toys and gave them to children for nothing. Krampus was surprised, because he was used to taking something from others, and not giving. The old man suggested that he try to diversify his life and make a gift to someone other than himself.

And so the deer did, gathering stones from the forest and giving them to passers-by. Of course, no one appreciated such generosity and did not accept the stone as a gift. Then the old man explained to Krampus that the gift must be sincere, and only in this case you will gain more than you gave. Then he decided to remove one of the trinkets from his horn and give it to the child. The first grateful smile inspired him. Krampus felt a surge of happiness. The joy of another made him joyful. Soon, all the trinkets were removed from the horns and given away. He made all the children in the village happy. When there was nothing left on his silvery horns, his heart became so light that he soared above the ground.

His suddenly discovered ability interested the old man. Krampus offered him his help in delivering gifts and gradually they moved further and further along the map until the news of them spread all over the world. But Krampus could not cope with such a load alone, and even the other reindeer in the team did not help much. The old man was very upset by this. He suggested that it was the silver antlers that gave the deer the ability to fly, and that if he broke them into several pieces, distributing them to other deer, they would have time to travel around the world.

Cutting off the antlers of a deer is like cutting off a person's hands. Krampus honestly told the old man that he was asking too much, because his horns would not grow back. The old man did not insist, but he did not resign himself.

A few days before the holiday, he invited Krampus to dinner, where he gave him sleeping pills, after which he fell asleep soundly. And when the deer woke up, his antlers were cut down at the root. It was not difficult to guess whose hands it was. Krampus was sad, angry and confused at the same time. Angry, he tried to take his horns back, but the nine deer, who divided them into parts, drove him away and maimed. They gouged out his eyes so that he would never find his way home. They cut out his tongue so that he could not tell the truth.

Krampus went deep into the forest, in place of his magic horns, as expected, no new ones grew. Then, instead of them, he tied two branches to them, inserted coals instead of eyes, and exchanged tongue with the wolf, allowing him to eat his heart. After that, no one saw him again, but the legends of the monstrous Krampus are still alive.