If its a OPEN show then it does not matter what you show it be it western or english. Most open shows with have classes that will state walk and favorite gait. Those are the classes I recommend. Also classes that state open Western or open english. Just means what ever horse your riding should be in western attire or english attire however in western attire or way of going usualy means the hosre should jog (slow trot) and not hard trot. Just compete in the clases that fit your match the closest. Open shows are just that OPEN to any breed or dicipline. Now if it states sanctioned TWH open show then its for registered TWH that show both Western or English and have classes to suit such. In Open shows the judge and what he or she likes is a crap shoot. Sometimes you never figure out what the Hell they like. In Open shows the judge may have never seen a TWH before or in some cases cant tell the difference between a goat and a horse. But they (open shows or fun shows) are usualy fun none the less and less stressful.
In breed specific or sanctioned shows you can still get a Judge that is more wishy washy than a washing machine but more than likely they are better educated about the breed being represented.
"The question is not, can they reason? nor, can they talk? but, can they suffer?" Jeremy Bentham