Unlike today when everyone wants a tan, women in previous centuries thought pale was prettier. Pale skin was a status symbol, since it showed that the woman did not have to labor outside in the fields like a peasant. But there is no evidence that women ate arsenic to lighten their skin. In fact, according to 18th-century apothecary specialist Robin Kipps, arsenic actually darkens the skin, so anyone trying this would have abandoned the effort quickly.
But some women did something just as bad. Since the early 1500s, some upper class European women (think Queen Elizabeth I) used a skin lightener called ceruse. Made with white lead, ceruse was also used in making paint. This probably caused damage, perhaps even death, if the woman applied it to her face often enough. It was still available in France in the middle 1700s, but there is no evidence that American women ever used it.