Why does metal feel colder than wood if they are both at room temperature?
Metal conducts heat faster than wood. Thus, the metal conducted heat away from your hand (or whatever) faster than wood.
The key word here is "feel". Just because they feel warm/cold, doesn't always mean that it is "warm/cold".
If they were both sitting at room temperature for a long time, then both will eventually reach the temperature of the room.
Even though they are the same temperature, the metal will feel colder than the wood because of the thermal conductivity of the metal, compared to the wood.
Metal will conduct the heat to your hand (or whatever you touched the metal with) faster.
On the other hand, wood is a poor conductor of heat and will slowly conduct the heat away from your hand (or whatever) much more slowly. It's so slow that it is noticeable (compared to the metal).
It is because the metal conducted heat faster that it feels colder than the wood, which conducted heat slower. They feel different temperatures, but they are actually the same.
Another example for the real world, is when you get out of the shower and step on the carpet - feels warmer. If you stepped on the tiles, it would feel colder because they conduct heat faster.
Hope this helps :)