There is no requirement by the British Show Pony Society to show a pony in a double bridle, and at Novice level the pony must be in a snaffle bridle.
At all levels the judge will take into consideration the severity of the bit used.
The Horse Bridle
If a double bridle is used the straps of the bridle should be small and neat and complement the pony’s head.
Usually the noseband and browband will be raised and patterned.
The bridoon and weymouth bits should also be small, with a short shank on the curb.
A Tom Thumb Weymouth would be ideal.
The show pony sets now generally available are finer than the general double bridle sets.
Running gags are not allowed alone or as part of a double bridle.
You must ensure the show pony rider has been given some training in how to use the double bridle properly.
If a child is nervous or inexperienced a better alternative is often the Rugby Pelham, which outwardly resembles a curb and bridoon but has a much less definite action.