If you get lucky and some hair and makeup guru wants to take you under his wing and train you in the ways of the craft, you may just be able to become a pro that way. However, a fine arts degree will be the much safer and reliable way to go. Even most acting majors have to take some courses in hair and makeup; your training, of course, would be much more extensive. That's right—you'll receive a hair extension.
Plus, you're an artist of sorts, so you really need to love what you do. Love the work, love the business, love the product. Not the hair product…gosh, does it always have to be about hair and makeup to you?