Since we don't know the exact 'baby reindeer original story', it could have the baby reindeer as the main character. Maybe its mother would also be an important character as she takes care of the baby. There could also be other reindeer in the herd like the father or the older siblings if it's a story that focuses on family relationships within the reindeer group.
If the 'baby reindeer original story' is about its growth and adventure, the main character is surely the baby reindeer itself. But there might be other characters too. For instance, a wise old owl that gives advice to the baby reindeer when it gets lost. Or perhaps a friendly arctic fox that at first seems like a threat but later turns out to be a helpful acquaintance. The baby reindeer's herd mates are also likely to be part of the story, especially if the story is about how the baby reindeer fits into the community of reindeer.