Is happiness a choice, or not? Must I pick a side? There is merit in both positions.
Certainly factors out of our control act on us all the time. To ignore the reality of the world around us would be, at best, wishful thinking, and immoral at worst.
But in the same breath I would quickly add that there is much under our control. We know that attitude makes a person who they are. To first address the ways in which we can foster our own happiness, I will give practical advice and examples, beyond a simple platitude to "stay positive" (as sincere as such an admonition may have been).
First, try meditation. The science on meditation is mostly in. The results seem almost too good to be true - meditation makes people unambiguously happier, more empathetic, calmer, and helps us to more easily concentrate. It can reduce stress and stave off panic. What does all this benefit cost? The pittance of ten minutes a day in restful silence. Meditation, a voluntary act, actually has the fascinating effect of altering the physical workings of the brain. In modern psychology and psychiatry, it is increasingly offered as a treatment of depression.
This is something nearly anyone, regardless of ability, can choose to do.
Another example of a voluntary choice that facilitates happiness is that of physical health. To the extent that we can choose to take care of our bodies and minds (meditation being only a particularly striking example of how), we can increase our happiness. Not only will being as healthy as we can manage ourselves help us be happy now, it will help us live longer, and thus be happier cumulatively, since we do not die as soon.
But this same personal aspect, health, is an equally compelling example of how it is not always in our control how happy we may be. To cut to the chase and give the most unambiguous example, imagine a head injury that affects the brain adversely. Specifically, it impedes the sensation of happiness, whether this is because of inhibited dopamine, or any other process that alters personality.
Do not doubt that this is entirely possible. In the famous case of Phineas Gage, the railroad foreman who lived twelve years after a railroad spike was driven through his front lobe, friends noted a change in personality so extreme that they thought of him as a different person.
If such a change occurred to any of us, and resultantly made us less happy in disposition, it could hardly be said to have been under our control.
It should not however be subsequently concluded that simply because some of our happiness is out of our reach to attain or retain, that we are absolved of the responsibility to ourselves and to others to strive to maximize our happiness as best we can. Even if my very skull is compromised, I can still meditate. I can still attempt to preserve my (likely fragile) health. Even if my last days of life are plainly before me, as in the case of a terminal patient, how happy we are in these last days is partly under our control.
Thus I answer that our happiness is under our control, but not fully. The most important part of the question, however, is certainly the part that recommends a course of action and lifestyle to us today and for the rest of our lives: you are not bound to suffer more than you must. Striving to be happier is never a futile pursuit, and thus should never be abandoned.