Open shows are usually run by clubs, I've been to open shows run by AQHA clubs and several run by Arabian clubs. Generally, by the area you are in and by what club is running the program is what I expect it to be. Like the AQHA club open show, definitely going to have an AQHA style judge. An AHA club open show will probably have more of an arabian style judge, or more of an open breed judge.
They usually have halter/showmanship in the morning, english in the middle, and western in the afternoon.
Since both your horses are young and maybe don't have as much exposure, ask if you can stall overnight. Come the night before, longe and expose them to the arena, and then they can rest and take in the sights and smells on their own.
Then you can be ready for halter and showmanship in the morning. Unless otherwise specified, halter is contingent on what breed you have, and SMS is always AQHA/western style.