Have programed into your phone your veterinarians daytime and after hours number. When your flustered it's hard to punch in the number. If your phone lacks that feature have the numbers written someplace by the phone.
You should become expert at taking your horses temperature, pulse and respiration. The vet will ask you what those vitals are, and to him/her, they provide critical details to what might be the problem.
That being said- if it involves an eye, a massive laceration, a suspect or active colic, a birthing issue, swollen windpipe, to name a few, the vet is summoned ASAP.
If it is a swollen, scraped or just a gimpy leg which halfway bears weight, the call waits until the following morning. After 30 plus years of owning horses I am comfortable making that decision. For swollen legs I will ice them or hydrotherapy them. Scrapes are attended to with water or saline solution first for cleaning. Then I might apply nitrofurazone on it topically and wrap if needed. For wrapping you would need brown guaze, vet wrap, elastakon tape and sterile telfa squares. Various femine hygine napkins make for excellent bandage supplies as do diapers so those are in my box. I will not bute if I intend to have it examined the following morning because bute will mask the underlying problem which I will be needing the vet to find. Have a good flashlight w/ a working battery nearby.
An eye condition can go to heck in a handbasket quickly. Those are best treated by your vet who might stain the eye to see if an ulcer is in it. It may be clogged tearducts which would have to be flushed. Never dink around w/ an eye problem.
My vet box is pretty much just basic bandage supplies because that is all I will treat without a vet's direction. If I think the lameness is an abscess trying to blow I'll put a soaking bandage on the hoof for a few days before calling the vet or farrier to locate it.
Hope this helps.