It depends on how you're doing it. If you're using a dresser and mirror, you'll have to change to the outfit you want to have a different hairstyle and then change the hairstyle using the mirror. Make sure to click off the lock in the upper right so that it won't change all of the hairstyles for every outfit.
If you're using CAS, you just need to unlock the hair options and switch between outfits and the hair options which is a lot easier than going in and out of the mirror.
Same goes for using a stylist makeover station as well. Both clothes and hair are available options and just switch outfits in the clothes section then choose the hair you want by going into that section.
