I would definatley check with the show and their rule book. Where I show, people usually just use a leather halter and leather chain lead (with the chain under the nose). The riders typically where their full huntseat outfit. Also, most showmanship horses are (almost exaggeratedly) groomed: hooves polished, super shiny, fake tails, braided/banded, and face glow.
Hope this helps and good luck showing!
Trends may have changed since I last showed English showmanship, but it used to be just a bridle for your horse and your full show outfit, helmet included. I did notice at the last palomino show I went to with a friend several years back that it was khakis and a blazer. Check with the people hosting the show if you're not sure.