What do scientists think the wrinkles on water-soaked fingers might be for?

Answer: Giving a better grip on wet objects

Letting the skin soak up water for the body — Wrinkled skin doesn't soak up water for the body; the outer layer is built to keep water out. The wrinkles appear even when the skin barely swells, because nerves drive them.

Keeping fingertips warm in water — Wrinkles don't keep fingertips warm; the narrowed blood vessels behind them actually bring in less warm blood. They also appear in warm baths, so protecting against cold isn't their job.

Giving a better grip on wet objects ✓ — The leading idea is grip: nerves narrow the fingertips' blood vessels on purpose, and the puckered skin may channel water away like tire treads. Some experiments found wrinkled fingers move wet objects faster, but others found no benefit, which is why the question is still open.