It really depends on the show. Our little local County Fair requires cowboy hats (helmets for riding classes for kids under 18), pants and a belt, boots with a heel, and a shirt with a collar. Most people simply wear button up western shirts.
Once I started discovering Western fashions being worn at bigger shows, I decided to go all out. My SIL, the little girl showing my pony, and I were the only ones wearing "fancy" clothes. It didn't bother us, but it may make a person feel out of place. Certain judges might've taken it as "showing off" (fortunately our judge liked our outfits).
The first year I went "fancy," I had a very small budget and decided to attempt to sew my own clothes. I bought show slinkies, but made blingy vests for myself, the little girl, and my SIL. Here was mine:
(you can't see it, but I'm wearing black "jean type" wranglers and Justin Roper boots).
The next year, the mother of the little girl decided to buy us clothing, so we got leather-like vests with blingy zippers and blinged out purple show slinkies:
(you can see my SIL in the back, I LOVE her vest)
And just because she's a lot cuter than me, the little girl:
In later years, I decided for less fuss and more comfort and just got a fancy-ish blouse to pair with my my black pants, belt & boots:
You can see my cousin, who's showing my QH for me, was much more casual, and that was perfectly acceptable.
As another example, here's a friend of mine wearing the type of outfit most exhibitors wore:
Most do wear black pants, but she was brave and went with tan. :)