Can I dip a soldering iron in water to cool it down?
Dipping the tip into water does not sound like a good idea.

However, you don't need to anyway.  I change tips occasionally on my soldering iron too.  Just use a pair of plyers to undo the nut, pull the tip out, and put in the holder.  You can use your fingers to put the new tip on, but will need the plyers again to tighten the nut.  The iron should be off when you do this, but there is no need to deliberately cool it.