Could you perhaps share some sources for women in Ancient Rome and Greece being expected to cover up? Is this restricted to certain areas/time periods/social classes?

Hello! Could you give a bit more detail on what you mean by "classical painting"? Frequently when people ask this question and specify painting, they are thinking of 18th or 19th century French paintings depicting nude female figures in mythological forms, such as those by Boucher, JL David, Canova, Cabanel, and/or Gerome, to start. Occasionally they're thinking of the some Renaissance paintings, such as those by Titian. If you are in fact thinking of art from antiquity, could you please be more specific? While I'm not an ancient art specialist I can say that aside from some specific representations of goddesses, such as the Venus de Milo and Aphrodite of Knidos, generally women were shown fully clothed in ancient Greek amphoras and sculptures as well as in Roman frescoes.