Yes, they do.  Shutters provide an extra layer of insulation.  We recently fitted some shutters for a couple in Rhyl.  We spoke to them just this week and they said that they  had noticed the difference in temperature in the bedroom where they’d had the shutters fitted.  It was a lot warmer in the bedroom during the cold spell last week than it was in the rest of the house.  Shutters not only keep a room warm, they also work in the opposite way to keep a room cool, which is how they originated.  Plantation shutters were developed in warmer climates to keep the rooms cool whilst still allowing through plenty of light.  This is just one of the benefits to having interior plantation shutters.