No, no and no. I have heard WAY too many stories of hair stylists in particular being AWOL on the wedding day and brides having to run searching for an (untested) replacement. A deposit, maybe, IF the hair dresser is coming to you. Full payment no. Think of it this way, when you call to make an appointment for something at the salon on any other regular day, do they take a credit card to hold the booking? No.