I don't understand this answer. Are you saying that there is no such thing as an "unhappy" song at all? That just the existence of art and creation itself is happiness? If so, I feel like it's pretty much irrelevant to the question of whether "Going Home" is a happy song, because there's no such thing as an unhappy song, and we have nothing to talk about.
In my point of view, a sad song is a song that makes me feel sad or sad-like feelings. As simple as that. It can be because of the lyrics, circumstances, melody, etc. A song that delivers a sad story and emotions. Usually, when I listen to a song, I'm more emotional than rational, and I don't think about the artist writing them. I think about the protagonist in them, and I feel their emotions. And a sad, yet optimistic song might be a sad one with a happy ending, for one example. And this specific movie, I don't have a solid opinion whether it's happy, sad, neutral.. So I wanted to hear you guys 
Anyway, as interesting as this philosophical discussion is, I feel like we're more in agreement than not since you did understand my question in a way that aligns with my meaning of a "sad song."
Yes, this is highly philosophical indeed, but not surprising since the subject itself is psychological and philosophical. We can take something that's famous for its sadness, like Albinoni's "Adagio in G minor", or the theme of the movie "Schindler's List", which is one of the saddest things humanity ever created, and try to analyse it. And like the war itself is probably the worst and the saddest thing humanity ever "created" as well, and still creates, in fact, war is, unfortunately, a big part of human civilisation and always will be. But ultimately, at the end of the day, it's how you look at things.
World War II gave us the technology and experience to launch, and get people into space, for instance. With the same piece of wood, you can either build a frame for a masterpiece, or a handle for an axe to cut someone's head off, “To every man is given the key to the gates of heaven; the same key opens the gates of hell.”
So this is what I meant by the ultimate happiness of any piece of art, even a very sad one. It's your choice, really. It can move you to tears, and it can be sad, or dark, but no matter what your choice is, life goes on, the sun will rise and shine, there should be laughter after pain, and there should be sunshine after rain.
And at the moment, Local Hero's ending could be sad or unhappy, which I don't think happened there, just like "Schindler's List" can leave you in a sea of tears, but you need to be able to leave everything behind and keep going, and celebrate the joy of being alive on planet Earth. Everybody deserves a Christmas present as Mark sang, "Gifts for each and every one In the Ragpicker's dream", it's about dignity, it's about happiness, it's about optimism in the best sense of the word.
