Yes. As far as I know, there's not much effect once you account for things like holidays or vacations (don't expect America to be getting much done in winter ie. December with Christmas, or France to get much done in late summer ie. July/August).

As it happens, I recently finished looking at my own personal data: I found no real* correlation of my self-rated mood/productivity with colder temperatures.

* The coefficients for the various variables are non-zero, of course, so one could argue that I found some small effects; but they didn't survive a complexity penalty and the estimates seem inconsistent to me: eg. there's a positive correlation between maximum daily temperature and minimum - but a negative correlation with mean daily temperature!