The best way to determine if stucco is painted or not is by getting it wet. just get a cup of water splash it on the wall or grab a hose and wet a area. if the color darkens and absorbs the water it is raw stucco, if ithe color doesn't change and the water beads or slides down the wall, it has been painted. Even I have to do this test sometimes as it can be fooling to a inexperienced eye. I've had to prove to homeowners that it was raw stucco because other painters told them it was painted.
Raw stucco doesn't need painting it is more cosmetic than anything, however there are a few cases that stucco does need painting so it is a case by case. Most likely it doesnt need painting it.
Note, once you paint stucco you should repaint every 5 years as a maintenance.
Woodwork should be painted every 5 to 8 years, if the wood is starting to split or twist and paint is peeling it is a indicator your waiting to long. its best to paint before it gets bad, less prep means less labor, less labor means less money.