Hello, this is Dr. Linda. I hope I can help with your question today.
This is certainly not a weird question. It is a very common injury with horses.
The first thing is to clean up the area. Clip any hair away from the wound & gently scrub using betadine or chlorhexidine. Rinse off any of the solution.
Running cool water is an excellent idea to keep swelling down. 10-15 minutes twice a day would be ideal. If there are any open wounds, you can use any topical antibiotic such as Neosporin, but the best would be a silver sulfadiazine burn ointment. However, you will need to obtain this through your veterinarian.
Bandaging would depend on how bad the area is, & if flies are still a problem. A light wrap would certainly provide protection & keep your antibiotic cream in contact with the skin longer.
If there is no significant swelling or lameness, then an antiinflmmatory like Bute may not be necessary, but start some if swelling does appear in the leg.
Other than this, you can probably care for your mare with what you have at home. It does not sound like you need to do injectable or oral antibiotics.
Just watch out for proud flesh, or exuberant granulation tissue that can develop on any wound on the lower leg of a horse. If your vet gets to that quickly, then it should not become a big problem.
Of course, if you are at all concerned about this, then a good hands on exam by your veterinarian is always a good idea, & I encourage you to have your mare looked at sooner than later.
I hope this makes sense & you find the information useful. Please let me know if you have any further questions or concerns.