I have a schooling show tomorrow, & I am not getting TOO dressed up. On May 31st, I have a competition at another barn (I just joined the adv. Showteam), but that's a real big show where you need to get all dressed up...
But at my barn, the schooling shows? Nope; you don't really have to go all out. Tails don't need to be braided, no special grooming (well, if you wanna you can lol), tan breeches, polo shirt (has to be white), jacket isn't really necessary, & make sure your boots are clean. You can wear your half-chaps if you wish, tall boots aren't required.
But not every barn is the same, so it just depends. :) I wouldn't go all out, though, just for a schooling show.
Ride more, worry less.