Stethoscope, thermometer, some sort of anti-bacterial cream, and eye wash.
Aluspray, vetwrap, duct tape, scissors, dressings, animalintex hibiscrub, clay poultice.
Bandages, creams like savlon, tcp etc, scissors, sticky tape, wound powder, green oils,.
Gauze/wraps, Band-Aids for the rider,poultice, thermometer, some type of first aid cream, antimicrobial spray, diapers.
Bandages of various sizes and shapes. A small pair of scissors. A poultice or two. Disinfectant/alcohol wipes. Iodine spray and/or blue spray. Baby nappies (for foot bandaging). Tape. Gamgee. Cotton wool. Hibiscrub or equivalent. Thermometer (labelled and with a string attached). Vaseline. Wraps to keep bandages clean. Vet wrap is always handy to have in case you run out of tape. Ice pack/heat pack. Disposable gloves. Sterile tweezers. Syringes.
I would also have the vets number taped to the side of the box, and a back up number if available.
Bare in mind also that some wounds take a long time to heal and may require several bandage changes so keep plenty of them supplies. Not long ago, we had a pony put his foot through a wire fence and cut his pastern. It took almost a month to heal, with two weeks of daily bandage changes. We needed enough wipes, bandages, cotton wool and wraps to keep us going for that long.