The short answer is yes. You need permission. Even if you see all sorts of stuff being taken and used on the internet. Even if it can't be policed properly, that doesn't make it right.

It's best to get permission for a couple of reasons. First, if you weren't the photographer, you are using the copyrighted work of the actual photographer. Copyright law specifies that it's the author who has the right to control how his or her work is used. And use of the work includes its republication on the internet in various salons. If the images were copyrighted, you could be held liable for copyright infringement and forced to pay damages. Second, you are playing off the image of the celebrity as a way of attracting people to your site, which is a violation of the celebrity's rights of publicity. A celebrity has the right to control how his or her likeness will be used in a commercial setting and it's likely that your online salon would fit within the category of commercial enterprises (not strictly an educational platform about hair). Think about it: You could just as easily find stock photos of hairstyles, pay the nominal royalty fee and use the image freely. You're looking to entice discussion by drawing people to the celebrity pictures. So you're playing off the celebrity as a way of becoming a discussion hub.