We have a small carry bag of grooming stuff--brushes, hoofpick, QuikClean, etc in our trailer in the tackroom in case we want to just go for a little excursion(say to a friends or a fun show).
We also keep ALL the grooming tools in one big plastic tub--grooming kit, show sheen(or other resident product), hoof polish(not really used at all yet), a big bottle of QuikClean, rags, harness cleaning stuff(in a ice cream bucket--very handy!), halters(big and small), lead ropes, twine(and lots of it!), ductape, scissors, shampoo and conditioner, yarn and braiding stuff...and the list goes on.
We also have two 'spares kits' that travel with the carts(usually on them) that contain a wrench, electrical tape, latigo, rein and trace splice, leatherman/awl/holepunch, another hoofpick, halter and leadrope. These are carried on all phases of a CDE in case of breakage or other failure.
I would also carry a full tool kit--screwdrivers, wrenchs, socket, etc. You never know....
We also carry a vet kit that stays in the horse trailer in case of problems or colic.
We always have extra helmets, whips, number holders, halters, wraps(legs), blankets, and leapropes in the trailer in case of an emergency.