Dry skin. Use vinegar to clean. When cooking organic and fowl, wash with liquid soap and dry with paper towels. Hands get rough and raw. What is cause?

Dry skin. Usual cause of dry skin is over exposure to water. The vinegar is Acetic Acid and though is good as an astringent, maybe too harsh for your hands.
Dryness. Raw skin comes from dryness. After cleaning and drying hands , apply a moisturizer[even crisco or vasaline will help.