It's actually a fairy tale called The Fir Tree, I have a book translated from the Danish by Patricia Crampton, illustrated by Sven Otto S, of Hans Christian Andersen's selected stuff. It's soo good. This particular one doesn't end with a happily ever after (turns out few of them really did. But they were heavily abridged especially during Victorian times when some of the stuff was considered too risque, etc)
I read the stuff when I was small but quite a bit of it went over my head XD although it was my favourite fairytale collection.
Anyway. I think my favourite story is The Snowman.