Also make sure you have extra stirrup leathers, bridle (or just some parts of a bridle), saddle pad, extra halter, medical bag.
A lot of people don’t bring an extra bridle but it is really good to have! My trainer has an OTTB who is very crazy and at one of her shows she took off with the bridle half on an broke it. My trainer didn’t have an extra bridle but luckily other people at the show had extra parts to help her fix it. It is something that can break easily and it is definitely a must-have for riding 😂
Bobby pins, hairnet, boot polish, baby powder (for white socks), spurs and crop (if needed), scissors, bailing twine, bridle and halter hooks, extra hair ties, raincoat, muck boots, a few rags, tack sponges, belt, and extra socks. Those are about the most common things I forget.