My mother hates my dad wearing his flat cap.  But as grass doesn't grow on a busy street (he's bald) some of us need just some upper protection from the elements.  Even those of us with a thick covering of turf will need to protect our head from the harshest mountain weather.

Heat loss from the head is about 33%.  A good hat is therefore imperative in the cold and wet.  Even in summer a hat is important and in this example is used to protect from incoming solarity and resulting sunburn.  However, even on a hot day, the summits are usually colder and the risk of heat loss can be an issue. As an aside, a -1 degree centigrade reduction in temperature on a winter day to -4 degrees centigrade is less of a problem than say a 8 degree reduction on a day when the temperature is 22.  In this latter example, a resultant wind chill could actually result in hypothermic tendancies as the body cools rapidly.  British mountains (Ben Nevis is the best example) experience the harshest climate at comparitive heights than almost anywhere in the world.  In some cases the comparison especially in the north should be to the tundra of the arctic not the European Alps.  Be prepared!