Living in AZ, I have had horses, and other animals bitten before.
A few years ago I posted about one of my mares that was bit on the nose one week before she foaled! IF I had not caught it about one minute after it happened, she would not be here today. It was early spring, when their venom is the worst, and she got it right on the nose. (This is usually where horses get bit too because they are curious so they want to see what it is making that noise!)
I got a vet on the phone right away, mine was out of town. Her first recommendation was to take a section of garden hose, and get it fed up the nostril on the side doing the least swelling. When I explained it was a Mini, she said no, a garden hose was too big. (duh)
My saving grace was that I have fish also, and my aquarium vaccuum is much smaller around that the garden hose- maybe 1/2 to 5/8ths around and more flexible than a garden hose too. I ran it, cut a piece and got it up her nostril. That was the only thing that saved her. She would have swelled completely shut and suffocated to death.
I then through her in the trailer and took her to the equine hospital, and after a large bill, there was not much they did for her really. They gave her a couple of things, which did NOT slow or stop the swelling- that just had to take it's course.
Edited to add: Keep some kind of good holding tape on hand too, because you are going to want to bend the tubing gently up and attach it to the side of a halter, and tape it there by the noseband. Elastikon tape will usually stick to anything!
She was so swollen her mouth would not close, but bless her heart, she ate soft foods anyway. I could hear her clear across the yard, sucking air in through that tube. It was just awful. She was swollen clear up past her eyeballs and it just broke my heart to watch her.
After two days, the tube started to get loose, and then the end of the third day it fell out on it's own! Yeah! The swelling was starting to go down!!
She foaled one week to the day after she got bit, and by that day, you would never have known what she had just been through. I prayed that she would NOT foal while she was so swollen and miserable. I dont know if she would have come through it ok.
Thank heavens she survived with no ill effects and no other problems. However, it depends on what type of rattler, what time of year, how old it is (the babies cannot control the venom release and usually shoot the whole thing), how much venom your horse gets when bit, etc... My neighbors had two bit by the same snake and lost one. The venom does damage to internal organs and she died, not of suffocation or infection, but because the venom caused her organs to shut down. It took several days and they did everything they could to save her, but couldnt. The other one healed up fine. They had two dog bit that year too, one made it, one didnt.
I will never again be without my aquarium tubing- it was just the right size for her nose (she is about 33.5") but you might want to look for something smaller for a Mini foal. (They do make aquarium tubing smaller too, but you want it big enough they can breathe thru though.
Our vets have never recommended anything that you can keep on hand to save their life in a pinch (besides making sure they can breathe). I have never seen anything that makes the swelling stop, or makes them feel any better. All you can do is hope they dont get a secondary infection, or that it does not cause damage internally to organs, etc... Once you are sure they can still get air, you have time to get them to a vet, or have a vet come to you, to see if anything else can be done.
By the way, that baby was named Snakecharmer!
I have never seen an animal partially paralyzed from a snake bite, or the results of it- though I am not saying it can't happen. The steroids mine was given did NOT stop the swelling, nor reduce it any, though I am sure they didnt hurt her either. I dont know anyone here that has ever used the antivenom.
Oh, another thing after being bit... make sure the horse is kept quiet while recooperating, and cool, if it is summer time. Maybe in a quiet stall with a quiet buddy next door. I soaked pellets and also fed equine sr while she was swollen and having trouble eating. It was easy for her to maneveur and get the food down.
Edited to add: Keep some good tape on hand too. You will want to gently bend the end of the tube up and tape it to the side of a halter to keep it in place. Elastikon tape is excellent. It sticks to ANYthing!