I don't show, but I've packed for many, many trail riding trips, and (used to) do close by and National CW Events.
Bring a duplicate of EVERYTHING. That means if you have an extra saddle and bridle and show pad, bring it. It's a Murphy's Law that stuff will break when you least expect it, and that can shatter your confidence in the ring to have to "jury rig" your equipment right before you enter the ring. 'O'
Extra clean clothes and gloves don't take up much space. If you have any extra gym bags there are great to pack in. You can leave the extras packed up for the next show, if you don't need to use them in a class.
ALWAYS pack extra hay and grain/supplements/meds/wraps or shipping boots, etc. We had BOTH our alternator and regulator go out on the way home one Sunday, and we were stuck parked at a garage that didn't open until Monday morning. I had NO extra hay, for 4 horses, and was lucky that it was a little town, and I could graze my horses in the adjacent, empty lot. I would pack enough extra food for 2 days, if I were you.
I used to have an extra, small garbage can for grain for my trips. I like the idea of prepackaging each day's feed. If you store it in a can in your tack room of your trailer, and it spills, it's easy to recover it at the bottom of the can, instead of on the ground.
Good luck at your show, and take lots of pictures to share with us. =D