I would not paint it dark for that purpose. Mainly because heat in the summer (if it is dark colored) is much more of a concern than being a little colder in the warmest parts of the day in the winter (if it is light colored).Mine isn't painted yet, but if I do should I paint it a dark color to attract more sunlight/warmth in winter? Would painting it a really dark color work like that?
Yes, painting it dark like that will make an observable difference in the temperature on sunny days - even if the coop has good ventilation (like an entire side completely open, if the other sides are closed so the wind doesn't whip through).