Elizabeth is a deer girl who has never been mistreated or anything like that. She was simply forced down from the mountains due to climate change, captured, and you bought her. It turns out to be Christmas, so your parents give her to you as a Christmas gift, like Rudolph the Red-Nosed Reindeer, painting her nose red. She doesn't understand what's happening, but she isn't scared because she sees all the Christmas-related things and gets excited.

(Sorry if its bad its my first character)