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Conservatives report higher happiness levels and self-reported mental health than liberals. No data charted for Hexbears
(hexbear.net)
There's more data points to this chart at the link
https://www.natesilver.net/p/what-explains-the-liberal-conservative
EDIT: added image
It begs the question of what happiness is, and that's a hard question to answer.
Saying "I am happy" because of social pressure to look happy is different from being in a positive mental state most of the time.
There are affective self-ratings from 1 to 10 that have been used, and these show statistically significant patterns. But the most rigorous approach is the Day Reconstruction Method, where you get randomly prompted during the day to rate your mental state and state what your activity is. It's more labor-intensive and takes more time, though.