Luckily, I've only had a face injury from falling off a horse once, and it was just a superficial (if rather extensive) abrasion on one cheek due to skidding on the arena footing.

If you ride again, and happen to come off, try to think about hitting the ground rolling. I know it's a lot easier said than done, but it's the best way to avoid hitting sensitive areas like faces and shoulder joints. You're far more likely to hit the ground on your butt!!

Which hurts, and isn't incredibly dignified, but is much better than most other options.