Am I the only one who thinks this has a happy ending?

Well, perhaps "bittersweet" is the better word. But yes, it's sad that she suffered from cold and hunger. It's sad that nobody helped her. So shouldn't we be happy that she escaped these hardships? Andersen himself says as much at the end of the story, or rather, the English translation says so: "No one imagined what beautiful things she had seen, nor into what glory she had entered with her grandmother, on New-year's day."

I think Hans Christian Andersen was one of those rare people who saw that death is not the terrible thing we usually make it out to be.

Still, I admit that I cried while watching this (and while reading the story), but it mostly wasn't from sadness.

Also, the music was a perfect fit.