Actually WDI (Walt Disney Imagineering) has a diversity of specialists working in its department. While engineers are a certain necessity and are arguably the backbone of the department, there is a vast diversity of educational backgrounds. Quoting from the book, Walt Disney Imagineering, written by the Imagineers themselves, "... Imagineering is a diverse collection of architects, engineers, artists, support staff members, writers, researchers, custodians, schedulers, estimators, machinists, financiers, model-makers, landscape designers, special effects and lighting designers, sound technicians, producers, carpenters, accountants, and filmmakers--we all have the honor of sharing the same unique title. Here, you will find only Imagineers."
Actually the first Imagineers were people Walt pulled directly from his film production crew. They weren't engineers at all. I highly suggest the book Walt Disney Imagineers. It's such an in depth book and you'll probably discover some task in their workflow you could be passionate about.
Also I would challenge Corrus's claim that they must be Masters degrees. I looked at Disney's career site under the Imagineering category for openings and none of them had this requirement. What IS a requirement is that for whatever position you're applying for, you have to be the best. If it takes you a Masters degree to get to that level, then so be it.