Hey Keely,
It depends on the horse. In the Classic division, I show most of my ponies in the same type halters I show my minis in. However, I have one stallion that needs a bit for extra control (It's actually a pacifier for him) so I show him in a bridle. In the Modern Pleasure division, most people show in a bridle.
Amber Montgomery would be an excellent person to ask for advice on this topic as well.