After being heavily involved with festivals recently (notably Latitude and Glastonbury) Id like to think I can offer a little advice.
From speaking and working with people throughout the chain, from spending time in meetings the Eavis's at Glastonbury to working things out with a stage manager on a small stage at Latitude there is one thing in common - these people love festivals and music. This is alot more important than a degree.
But the real question you should be asking is "where do I want to fit in?" Accounts? Stage management? Bookings? General organisation (ie location of stages, ordering toilets etc)
Specialist areas such as financial management - it would probably be wise to do a relevant degree.
The bookings people just need to be able to recognise good music, although experience in this, or in finances/businesses etc is still important.
Basically - if festival management is your dream, do a degree in business and management or event management - it will stand you in much better stead. But if changing isnt what you want to do, or is to hard, you will be able to get involved in festivals without a degree!