Your body senses temperature as how quickly heat is leaving your body. Very slow heat transfer means “The air / this thing is almost as hot as I am!” Very fast heat transfer means “The air / this thing is much colder than I am!”
Metal and water are much, much better at accepting heat than wood or cloth are. Thus, even at the same temperature, they “feel” colder, because they are still sucking heat out faster.
(Conversely, this is also why, *above* body temperature, hot metal and hot water are more painful or burn you faster than hot wood or hot cloth do! They give up their heat to you faster as well.)
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