Let go, I've almost had a horse fall on top of me because I dragged him down coz my hand was caught in the reigns. If you horse runs away, that's ok you just gotta go looking for them, some people are worries about their horses tripping or getting caught in the reign s when they're bolting but if you think about it, the leather or stitching will break
I agree with Lucy, holding on to the reins could hurt the horse. I am a master-accidental-dismounter (I fall a lot) and the best thing I have done is wrap your legs tight around the horse and grab a handful of mane. A horses mane has no feeling in it. When I was little I actually hung from my horses mane as an experiment. I don't recommend that, because I could have ripped all the hair out but anyway, also try to land on your feet/butt/shoulder (tuck and roll)
A lot of people are saying yes, you should, but I never hold the reins when I'm about to fall, ESPECIALLY if the horse has a bit in his mouth.
When you fall, instinct is to grab tight onto the reins, but when you do this the horse has to deal with his mouth being yanked which is extremely painful and has caused severe injury before. Seeing a horses mouth bleed due to someone falling holding tight reins changes your mind very quickly.
If you're out hacking I would say to hold on as to avoid losing your horse - but in a schooling arena I'd say let go.
There's a lot more risk to both you and the horse if you hold on, including that you get dragged, the horse suffers a mouth injury or you get tangled in the reins.
You should hold onto the reins during the fall and let go after. You usually can't hold onto the reins after you fall and if you do let go because if your horse keeps going you can get dragged. You should try to hold onto the reins during your fall because that helps you fall on your bum and puts less impact on all the other body parts. This is the safest way to fall.
If you know that you're going to fall, you shouldn't try to let go of the reins unless you think you might be able to stay on. If you hold on, just like @kaitlyn2
said, you could get dragged. You also pull on the reins which can cause problems with the horse or wrench your shoulder.
During yes. After no, due to the possibility of the horse continuing and dragging you along with it. Hope this helped!