It would be really nice if we could change our characters hair style for crowns or gold because it can be annoying when you regret choosing a certain hairstyle.
If you go in the Crowns shop under hairstyles, there are many to choose from. Once you get the style you'd prefer, you can stitch it onto any hat.
If you meant that you'd like to permanently change your wizard's hair, many have asked for that ability but KI hasn't offered us that opportunity yet....
Alia Misthaven