You can only catch a cold by being exposed to a virus. By being cold, (in cold weather, or with wet hair) you place a strain on your body, so it has to divert some of it's energy to keeping you warm, rather than fighting infection. So you can make yourself more susceptible to a virus you've contracted by going out with wet hair in the cold. But if there is no virus present, you could stand all day naked with wet hair in freezing temps and not catch a cold
This is kind of a wives tale. The only reason they say you can catch a cold in the cold is due to the fact that once exposed, the cold or flu virus survives longer in colder situations. At least that's what dr oz said!