Riding in the rain? Sure. A thunderstorm? Oh heck no!
I have synthetic tack (except for my bridles), so getting caught in the rain is no biggie for me. The horse and I aren't going to drown.
Lightning though, I'm not that
foolish to venture out into willingly.
We got caught in a thunderstorm when we were riding in the Grand Tetons, and let me tell you, THAT was a hair raising experience! Thunderstorms are really, really close when you're riding at 6,000 feet!
We took shelter in a deserted hunting camp, although we left the horses tied outside. I fretted about it, but we couldn't bring them into the tents.