Ponies don't need to take showers very often. A storm might do the trick, and they're getting dirty all the time, anyway. Being ponies all their lives, the Dazzlings didn't worry to much about staying clean.
Adagio Dazzle, Aria Blaze, and Sonata Dusk have no clue when it comes to human hygiene, though. When people say the Dazzlings stink, they mean literally.