Andsersen has some happy endings, eg the Snow Queen or the Ugly Duckling. I guess the Matchstick Girl has the closest to a “happily ever after” ending, since she dies and goes to heaven.

Death usually is a happy ending in his stories. It's ascension to paradise and being freed from mortal suffering. It makes more sense if you're a deeply religious man from the 19th century than it does today, admittedly.