How about this: do go to art school†, and do study programming as well‡. I went to school for design—interactive media, specifically—because I was already experienced enough with programming and wanted to learn something different. Even though I took on some nontrivial debt, ultimately it didn’t matter because programming pays the bills. All you have to do is accept the golden handcuffs for a year or two. And you know what? I gained an immense amount of cross-disciplinary knowledge and experience, and had a lot of fun to boot. There is just as much value in being “an X who can program” as there is being “a programmer who can X”.

† though preferably one less expensive than RISD

‡ on your own time, not in a college setting