Why do your skin of fingures shrink when you wash clothes for long?

Actually the wrinkles fingers get when in hot water or while handling soap or detergent for a long time is not due to skin shrinking, or even drying up like a mummy for that matter.

Oil and water don't mix, and skin has a protective layer of oil which hot water and soap ends up removing. Hot water because the surface tension is lessened, so more weak intermolecular bonds can be formed and soap because it contains big molecules which due to surface area also forms many intermolecular bonds. Both end up solubilizing the oil, which removes it when the water is washed away.

What happens the the fingers when they wrinkle is the water goes into the through the skin, and swells it slightly.