In California, so different type of rattlesnake, but I’ve dealt with a horse, two dogs, and a cat that have all been bitten. Pain meds, anti-inflammatories (steroid and non- ), antibiotics, are standard treatment. It is too late to do anti-venom, nor should it be done unless you are SURE it was a rattlesnake. At this point, swelling isn’t bad, there is no real point to do anti-venom, it is more about reducing acute swelling (for example, our dog’s leg swelled so much, so quickly, there was danger of it splitting open). The cost to do anti-venom on a horse would be - horrific! It is based on animal weight.
I would ask about putting the horse on an oral broad-spectrum antibiotic - I think we used SMZ on my horse. Also used orals on the dogs and cat.
You are out of the danger zone for necrotic skin in about a week to 10 days.
We have a lot of rattlesnakes here in the foothills of Nor-Cal - my vet treats quite a few snake bites, and said most bigger animals survive - they have so much body mass to absorb the venom, it isn’t as deadly as it is with smaller animals or children. The risk is the necrotic tissue. My horse survived with no long term issues at all, whew… Our cat and one dog survived with no issues too, but the other dog didn’t - he had secondary immune system problems as a result of the bite, and made it a few months before we had to put him to sleep.