You can't live in fear. If there was concern about a rabid or diseased animal out there, I can see holding off on trails until the animal was caught. But wildlife is wildlife and it doesn't go away. I would still ride, but I would pack some protection. In Georgia, I carried a .22 revolver. I don't carry anything now that I'm back in Pennsylvania. You bet I'd carry at least an air horn if there was a cougar in the area though.
Just don't freeze your enjoyment because of fear. Nothing has changed other than the fact that you know what's out there. So, prepare for it.
It's not hard to desensitize your horse to an air horn.