I checked sunlight hours, average annual temperature, and seasonal temperature standard deviation (i.e. extremeness of seasons) against Gallup well-being data by metropolitan area, and state-level Gallup Healthways happiness data. The scatterplots were a mess (no point in even showing them here) and there was no relationship.
This struck me as very good news actually. Yes, maybe a change might have an effect (a particularly severe winter may depress you if you're not used to it; a week or two in the sunny Southwest might lift your spirits if you're stuck in a dim Pennsylvania winter). But of course there's the infamous hedonic treadmill effect, which is actually good news. Wherever you're living, it's likely the people and the work you're doing there that's determining your happiness, rather than something superfluous like how warm and sunny it is.