As a new mummy, one of the most frequent reminders that I get from the elderly around me is to reduce the chances of baby catching a cold. Examples of the suggestions I receive is to ensure that the windows are closed and switching off the fan while giving baby a shower.
While I do believe in switching off the fan, I do not see the need of closing the windows unless it is raining cats and dogs outside and it is very windy.
A more effective way, in my personal opinion, is to ensure that the temperature of water is not kept too high. Otherwise, there will be a contrast in the water and the room temperature. In this way, chances of baby catching cold during shower will be kept to minimum.