What you carry, can depend on what you are doing with the horse. I started with the basic Pony Club list of First Aid stuff needed for Rally. You can probably find that in the list of Required Equipment in the Rally books on the Pony Club site.
I have added and modified other contents for things that we use our horses for, which might be Trail Riding, going down the road hauling, as well as show sites.
A couple important items were the two, loop ended, 20ft nylon tow straps for pulling equines who are down and stuck. Learned about them at an Emergency Training session related to horse barns. Sounds awful, but we have used those straps now about 6 times since the class! Old horse gets herself stuck and the straps work like a charm to roll her over, slide her up and out of the ditch. She is quite embarrassed, but uninjured with those pulls using straps.
Most of my stuff can be used on people or horses, if the need arises. I keep things in a 18gal. Rubbermaid tote in RED, easily located by "anyone" sent to get it from the trailer. I also put the "pieces-parts" in containers, like zip-lock bags, those Gladware boxes, so you can see the items, but they are protected if the box gets knocked over so everything spills on the ground. I write on the bags and boxes to label them. I also have the Horse First Aid book in the bottom, should I need more help than my experiences cover.
Cutting corners, I use the wrist and ankle wrapping tape instead of adhesive tape. Buying rolls in larger containers make the wrap tape cheaper. It also rips off easily, can be ripped narrow if needed. Another item is buying quilt batting in cotton, cutting it to fit for wrapping legs. Not sterile, but plenty good for wrapping over the covered wound, stiffening up a leg or under bandages. Cotton gauze in wide (6") rolls. I get the cheap, non-sterile from places like Omaha Vaccine, where you have to ask for it, not in the catalog. Again, used to hold wound covering in place, sterile really is not needed. I carry a LOT of Telfa pads for wound covering, usually in the bigger size, 3x4". Stack of sterile gauze pads, should you need to put pressure on a wound or need stuff to soak up blood, serum from the wound. You can wrap the pads into wound cover after putting on the Telfa cover over hole. You can cut Telfa pad down or fold it, if they are too big. Several rolls of Vetwrap type wrapping. Several polo wraps and true flannel bandages. Another recent addition is Super Glue or it's generic equivalent. You can do a LOT with Superglue to hold wounds closed when you can't stitch.
The other basic stuff, Antibiotic Ointment, Hydrocortisone cream (kills itches), good pair of heavy scissors with the metal flap edge for cutting bandages and almost anything else you aim them at! Cheap at $4 from TSC. Thermometer. I have old mercury ones and new digital ones that are much faster. I got a duck face one for $3 on sale, plus probe covers. Vasaline for those old thermometers, since I never have enough spit. Large, pointed tweezers, locking hemostats with narrow pointy ends for cleaning holes. A small, folded up Space Blanket, unfolds big enough to cover a horse or person if needed. Small package of paper towels or real hand towels to wipe stuff off with.
I carry a small bar of Dial soap, small bottle of Phisoderm baby soap, small bottle of distilled water and a bottle of saline solution, for washing holes, your hands, as you care for horse. You might want to include a twitch that will fit in the box, could be needed. I have included a couple of cold packs and heat packs, that work when you snap them. Have come in handy for people who sprained things at the show. Stethecope that works.
Taped inside the lid of box is list of normal temps for horse, list of box contents and quantities, so I can refill as things get used.
Oddly enough, in my tool boxes on the trailers, I carry two hacksaws. I was part of some folk trying to get a horse out of a stock trailer AFTER horse kicked thru the bars of the center gate!! There was just NO WAY to get that hind leg out, unless you could have sawed the bars. There were no hacksaws at farm anyone could locate, so the Fire Dept. in FULL-GEAR came with Jaws-of-Life to bend the bars, make a big hole to pull hoof out of. They got leg loose about the same time Vet arrived to care for the injury. So now I carry a regular frame hacksaw and one that can cut using just the blade and handle, no frame, fits in TINY spaces for cutting things. They have SHARP blades on them. May never need them, but they don't take up much space and I AM READY if another horse does such a dumb thing again.
You can add in Meds of your choice, don't forget to pack syringes and needles to give it!
We do seem to end up in the middle when there is "an incident" needing medical care. Our box is packed for things we have had to deal with in the past. You might never see those kind of problems, or at least I hope not!
Lovely thing about making your own First Aid box is that you can tailor it to your needs! That isn't everything I have in the box, but a good starter list for ideas.
My vet recommended a tube of banamine. Otherwise I have the basic first aid kit stuff, kept in a bucket with a lid. In a pinch, the bucket can serve for holding water to wash things with if needed. I love the hacksaw idea, goodhors, and will add that to my trailer kit this afternoon!