If he is entire he will need a bridle. I show my yearling colt in a filly slip but next year he will wear a bridle, some schedules state that colts and stallions must be suitably bitted. If he is a gelding then i don't think it matters.
''Colts and stallions of two years old or over must be shown bitted.
Younger animals and older females may be shown in a suitable leather headcollar.
For in-hand showing, only plain English-style jointed or straight bar snaffles are permitted. This includes the Metropolitan/ Horseshoe Liverpool bit often refered to as a stallion show bit.
In lead rein classes ponies must be shown in a suitable snaffle bridle with the reins going directly from the bit to the riders hands. The lead rein must be attached to the nose band only. Whips or show canes carried must not exceed 30 in length.''
Hope the above helps, it's taken from the SSBS.
We used to show minitures, our geldings and mares were always shown in a show bridle and bitted.