We've always given all our horses their 4-way shot every year. And we've also been doing West Nile every year, once that started becoming an issue again in recent years.
The only reaction we ever had was with my horse, a couple years ago, was having some stocking-up leg swelling issues for a couple weeks after I vacinnated him. However, he was also being kept in a small, small paddock because the people I boarded with were trying to give the pasture grass time to grow. I suspect that since that was the only year he was not allowed to freely move around and keep circulated, that it had something to do with it. He's been fine any other time.
I would either take your horse to the vet and have the vet do it, or have the vet come to your house. (Usually cheaper to bring your horse to the vet.)
Vaccinations for horses are like vaccinations for people. Yes, there is a chance of side effects. Yes, there is a chance you can get sick from it. But I'd rather just have the vaccination, since those risks are small.