Lifelong avid horseman here as well, V. I'm a volunteer wrangler and trail guide for a 4200 acre ranch with almost 200 horses. At the end of the day, all are turned out into a very large pasture, so wildlife encounters are common. Except for the occasional skunk though, all of these encounters are harmless, and some are downright funny.
Bobcats aren't likely to be a problem for horses, the exception possibly being a very young foal when mom isn't around. They can and do take down an occasional small deer, but they mainly eat rabbits & rodents.
Horses have the advantage of size, speed and strength. There's just no way that a 35 pound, 3 foot long cat can be much of a threat to a thousand pound horse, and I doubt that they'd even try. Any that do would most likely end up stomped into a [color=#FF0000]█[/color][color=#FF0000]█[/color][color=#FF0000]█[/color][color=#FF0000]█[/color][color=#FF0000]█[/color] pancake.
In the unlikely event that you'd encounter an exception (say a rabid cat), a .22 will do the job. I'd listen to the wildlife folks though. Killing a protected species without a really good reason will definitely land you in the pokey.
There's more info on bobcats
here.
All that said, this is more appropriate for The Hunt forum, so I've moved it there.