The choice whether you wear your hat is up to you. In my time period the kings of England only wore their crowns on special days and it would had been improper to wear something if your king is not wearing anything. Have you noticed that many of our dukes only wear their coronets at high court. The Roses wear theirs most of the time but mainly as a way to finish off our garb. They are great for keeping veils on. They also solve the problem of what to do with your hair. Some people, like me wear period coronets that look like SCA  baronial coronets. Be warned if you don't wear your "hat" or you do like I do and not wear the correct SCA coronet. It will be very possible that people will not address you by your proper title. If this is going to bother you please help people out and wear your coronet. In the SCA many barons put their coronets on their regular hats, but my studies suggest this is not a period style. Look at today's customs most nobles in England only wear their hats in full court situations and they don't wear them with hats. 
Duchess Willow de Wisp