Not that I know of. My horse is barefoot and he does dressage shows. It would be wise to double check with the organization that is holding the show, but I highly doubt that you need shoes.
In response to the off topic discussion on here about prices: I get my horse trimmed every 6-8 weeks for $50. If I wanted him shod, it would be $150. Barry, there are expensive prices over here too. It isn't country related, it just depends on what kind of place you are living in (ie farmland usually has cheaper prices while urban areas have expensive prices).