Yeah, this is something that bugs me. I often hear people say about depressed people, "You're just making yourself miserable, you WANT to be unhappy, you are choosing this." There are those out there who may enjoy being miserable in a twisted sort of way (maybe the attention or whatever), and then there are those who want to be happy and feel normal but who maybe do have a chemical imbalance, or perhaps they aren't able to get over something traumatic, who knows. Each person experiences things in their own way. Who is any one person to tell another person that something "isn't that bad"? Countless times I have heard people say, "If you want to commit suicide you're crazy, come on your life isn't that bad." How do you know??? I mean, really. What you see on the outside means very little in the grand scheme of things, when it comes to how happy or unhappy someone is.
So saying, it is true that there are always choices of SOME sort to make, involving your happiness. It could be the choice to get professional help if you have lingering depression. If you do nothing about it, well then you are truly making the choice to REMAIN unhappy. Let's say you make the choice to try and learn better coping skills. What if a certain approach doesn't work? I don't think that means you are still choosing to be unhappy, if you are still depressed. I think it means that you are struggling with something you don't fully understand yourself, but as long as you are actively pursuing ways to get better or figure it out, you are choosing to pursue happiness.
In short, I don't think people choose from moment to moment if they are happy or not. I think what they do is make choices in the present that will affect how they feel in the long run. THAT, in my opinion, is choosing whether or not to be happy. But, and again this is just my opinion, I think it is a bit ridiculous for anyone to think that everyone everyday is choosing to be happy or unhappy. IF anyone even thinks that at all. I'm probably reading into it too much, as usual

I guess it's sort of a vague question. A bit broad, open for interpretation.