Question

why does an iron chair feel colder than a wooden chair in winter

Answer 1

Iron is a better conductor of cold than wood. For the same reason wood will burn faster and easier, because it is a better heat conductor than steel.

Answer 2

Iron is a good conductor of heat. Since our body temperature is warmer, the iron chair absorbs more heat as compared to wooden chair (since wooden chair is comparatively bad conductor of heat). Hence an iron chair feels cooler than a wooden chair in winter.