Spare underwear and breeches. Not saying you are going to poop yourself or anything, but all kinds of s*%# can happen at a horse show. My old boss once had to show with her pants duct taped shut after they blew a big hole 
So I guess I would add tape to that list… even if your barn probably has some, you can never have too much tape and you might even make some friends by having it handy. All kinds. Duct, masking, and especially black electrical tape (not that boot zippers ever break at a horse show or anything
).
I can’t reiterate socks enough. For all things in life. Spare socks. For a horse show, lots.
Band aids, maybe even a little first aid kit (I say as the person who usually uses the above mentioned duct tape to stop my bleeding… be better prepared than me!)
Hair brush, extra elastics. Deoderant. Face wipes/microfiber towels. Any other toiletries you may like to get through a day feeling like you aren’t wearing a sand ring or were rolling in your horse’s stall.
Clothes for every season, even if it’s not the one your show occurs in. Maybe this is more Canada-specific, but it happens all the time, people ending up cold, wet, or hot when the weather doesn’t do what it is “supposed to”. Rain gear! Jackets, sweaters, even gloves and warm hats. And on the flip side of that… sun hats, T-shirts. Shorts and tank tops to change into after showing. If there’s any chance of it being warm and you’re prone to overheat, then cooling gear like the neck wraps and headbands you can soak are something worth considering.
If you want to save some moola (to buy more fun things from the vendors), I recommend bringing ample drinks and snacks. It’s one thing to give in to the horse show food for lunch, but it’s the extras where they get you. If you are into healthy snacks, definitely bring them, because there may be limited options. But… if you know you’ll probably cave to junk food anyway, you’re probably better off to bring a $1 chocolate bar with you than pay $2.50 at the show.
Phone charger.
Good luck and have fun!