I thought about going to a school specifically for photography, but I found that working for and learning from professional photographers was a much better way to learn and grow than learning in a classroom environment. I think there are certain fields where going to an art school would definitely be beneficial. Like Shiny mentioned, things like animation, film, etc. But not so much for things like painting or photography. The best part of having a formal education in the arts is that you're constantly being forced to do new projects, to meet deadlines, to expand your horizons, and learn new techniques. And you'll probably learn at a much faster rate than you would if you tried to teach yourself. And especially for things like animation and film, you would have access to equipment and software that you probably wouldn't if you weren't a student.

But with something like photography, you just need a camera, maybe a good mentor and you just run with it.