Why does metal feel colder than wood at the same temperature?

Your skin does not measure temperature directly. It senses how quickly heat is leaving or entering it, which is a very different quantity. Metal is an excellent thermal conductor, so when you touch it, heat flows rapidly out of your hand into the metal, and your nerves report that fast heat loss as cold. Wood, plastic, and fabric are poor conductors, so heat leaves your hand slowly and the same object at the same temperature registers as neutral or even warm. Put a thermometer on both and they read identically; put your hand on both and they feel nothing alike.

This explains a set of everyday experiences at once. A tile floor feels freezing while the rug beside it feels fine. A metal spoon left in a drawer feels cold, a wooden one does not. Getting into a car in winter, the metal seatbelt buckle is punishing while the fabric seat is merely cool. It also runs the other direction: metal in the sun feels scorching not only because it is hot but because it dumps heat into your skin fast, which is why a metal slide burns and a plastic one at the same temperature does not. The same principle explains why water feels colder than air at the same temperature, water carries heat away from your body far more efficiently, which is also why hypothermia sets in dramatically faster in cold water than in cold air.