I’m curious, do you have any first aiders that hunt that members are aware of? Are basic first aid kits carried on horseback (saddle blankets with pockets), or in a vehicle that follows the field?
I’ve never seen it but have done first aid on both horse and human with stock tie and pin.
My sandwich case always contain the following: role of vet wrap for small injuries that needed wrapping because I would never use my stock tie or pin, antihistamines for bee stings, bandages for small wounds, a folding knife, small wire cutters, and a piece of baling twine ( because that can always come in handy).
We have a paramedic and a couple of medical doctors in our hunt, but I do not think any of them carry a specific first aid kit. I have ridden with our road whip quite a few times and I don’t think she has a first aid kit in the car, but it might be tucked away somewhere.
Many of us carry things like vet wrap, knives, antihistamines, gauze, etc in our sandwich cases. Between us all, we could probably supply a minor surgical procedure. 
When I started whipping last year, I made a kit containing: gauze, rubber gloves, vet wrap, and a small tube of antibiotic ointment in case I needed to treat a hound out in the middle of nowhere. I also carry advil, antihistamines, and an epi-pen (for my bee allergy).
Many of our members/staff work in the medical profession and quite a lot of our garb is intended for vet/medical use (stock ties and pins, belts, stirrup leathers). I keep first aid items in my trailer and none of our properties are so large that it would be much of a time constraint to head to the trailer to get them in an emergency.
We just have small stuff on hand: first aid kit in the hound truck, some of us have them in our trailers, and many of us carry small items like wire cutters, knives, and vet wrap. We also know who is riding that day and has training.
More useful are the lists of phone numbers for nearby emergency vets, addresses where an ambulance can pull in, and maps of where/how to reach a human or equine who is badly injured and shouldn’t/can’t be moved. Ice and aspirin are available at the kennel house–it’s the serious stuff that needs real planning.
I always carry Benedryl, especially in the fall when we hit a lot of ground bees.
I think you will find that there are usually some doctors/nurses out hunting and every trailer should have first aid supplies for horses and humans. Once you know the extent of the emergency, you either use a follower in a car or call in the emergency services.
I’ve been with my hunt club for 10 years and we’ve had our small share of rider or horses cuts, low blood sugar, unexpected wire and so on that have been managed successfully.
There is one tool that should be in every field- one person who knows how to properly perform CPR. A few years back a member had a need for that skill and two other hunt members saved the other members life by performing CPR for 20 minutes until medical transport arrived. Yes, 20 minutes of CPR, an extended stay in ICU and God’s grace kept the affected member alive.
I understand that the purpose of stock ties and pins were made for just that reason - as a medical aid if you have an injury in the field.
I ride in the truck with the road whip; we have first aid supplies for horses, riders and hounds including Benadryl, Payday candy bars (for low blood sugar), and drinking water. We have even more supplies at the trailers. So far in the 5 years I’ve ridden in the truck we’ve only needed to give first aid to a hound to stop a bleeding wound.
