Yes, you can still get mood-lifting, immunity-boosting vitamin D on a cloudy day. Full-spectrum sun is still happening behind that gray, cloud cover and the ultraviolet needed to trigger the synthesis of vitamin D is still evident.

It’s still necessary to practice safe sunbathing practices, because it’s possible to overexpose on these days too. But safe sunbathing doesn’t mean covering your skin with sunscreen. The best sun protection is gradually building your own natural sunscreen, your melatonin, rather than exposing your skin to the manufactured toxins in many man-made sunscreens.

Winter in most parts of the world tends to be the rainy season, with less sunlight, more cloud cover. And in the far north, Arctic Circle and above, the sun barely shows itself. The lack of sun exposure results in high rates of seasonal affective disorder (SAD), a recurring depression that usually presents between fall to winter. Many people with SAD have insufficient or deficient levels of Vitamin D. (1)

Studies show that a one-hour walk outside, even in overcast conditions, will eliminate the symptoms in most people diagnosed with this disorder. The level of ultraviolet light was sufficient enough to stimulate the production of vitamin D and result in a brighter mood. 

So the answer to happiness is sunlight - whether it's yellow or gray...