They've been broken for a while ago already. I believe it was mentioned in a previous announcments about wardrobes that neither the hair saloon nor the tanning saloon would work.
As I've noticed, you can still put any hair from the hair saloon or any skin from the tanning one but you won't have a preview. For the hair saloon, what I've been doing is making guesses and putting the color I want and then save and then I am charged the 10,000sP and then I go to some other page and do CTRL+F5 which is a mayor refresh and I see the new hair with the colors I chose. If I don't like them I go to the wardrobe again and change the color and so on. It is a expensive way but as wardrobe is going to change, it's the only way for now.
[edit] You will not also see the new hair when changing clothes with the old wardrobe. If you want to see the new hair, you must use the new wardrobe. If you don't see it at first, it's because of the caché and you must wait or do the mayor refresh I already mentioned.

As said above this is an ongoing issue that we all hope will be fixed with the new wardrobe. There is an open error board for this issue that you are welcome to post on. As soon as we get any status updates we will let everyone know! Thank you for your patience! Locking as duplicate topic.
Dexter by ❤