Anywhere far enough north for loss of egg-laying to be an issue during short winter days... and OH does qualify for this, IMO... it is generally better to use a light color inside the coop. If you are adding supplemental light it allows you to use lower wattage (cheaper and safer); if you are NOT adding supplemental light, it minimizes the number of weeks during which the chickens' bodies will percieve there to be too-short days to lay.
As far as effects of red painted interior on chicken behavior, there are good arguments both pro and con, I have not seen results of any actual quantitative testing of the outcome (tho it may exist somewhere, I dunno).... but personally I'd be leery of doing the experiment myself on my own chickens, as there is definitely the possibility of it instilling bad habits.
JMHO, good luck have fun,
Pat