I remember reading a picture book when I was a kid, it was a story about a boy who lived in a snowy area and he was searching for his father. Along the journey, he defeats an animal and uses its horns/claws/teeth? And uses them to skate across a frozen lake bed and finds his father. The boy was relieved to find his father, but the father told him that it was too late, that he had run out of time or something. The book was fairly short, unfortunately that’s all I remember from the story. I remember reading it sometime around 1992-1999, when I was in elementary school, but no idea when the book itself was published. I have always remembered the book every Christmas, but could never find it.
Other details that I can think of is that the story initially starts off with the boy and his mother in a wooden cabin as she is preparing dinner(?). The boy asks the mom where the father is and eventually goes out to look for him.
Please let me know if you require any more details, I will be sure to let you know if I can remember anything else.