dishpan hands

(idiomatic) Hands which are rough, reddish, and dry, as from irritation and chafing caused by immersion in hot water mixed with detergent.

Example: 2007, H. E. Thomas and M. Thomas, "5 Ways to Combat Cold-Weather Hands," Washington Post, 18 Feb. (retrieved 30 July 2009):
  Avoid dishpan hands. Those 1950s sitcom moms had it right (and probably had lovely hands): Wear rubber gloves while cleaning and doing dishes.