I would say anywhere from $500- $1000, and maybe more if anything more serious is involved. I say $1000 just because you never know if your horse needs to stay at the vet for intensive care, meaning daily board and care at the vets office, plus treatment.
I would say at least $500. That would give you a nice down payment if anything worse happens. I would not stop there, just keep adding to it. I have a fund that any extra $$ I come across goes in, like birthday, tax refund, even if I return anything to the store the cash I get back goes into my kitty. It is good for saving $$ too.
I have had a $300 vet bill turn into a $1500 vet bill within 5 days after the vet left due to a infection in the leg. So you never know. I would say atleast $1000 set aside maybe more. Its always nice to have a nice cushion to fall on if things hit the fan.