When you are in the bath how come only your hands and feet get wrinkly?

"Anchored" skin: Palm and sole skin is more tightly attached to the underlying fascia; elsewhere it just slides off, but on palms and soles it has no place to go when it swells with absorbed water.

Thicker epidermis: The epidermal layer of the skin is thicker for protectie mechanisms and therefore will absorb more moisture and create the wrinkling effect.