most horses have very little or no sensation on their manes (although there are a few who dont like to have their manes "pulled")...but as long as they havent rubbed themselves raw through something like sweetitch, a horse (I should think), would be MUCH more appreciative of the rider holding on to their "numb" manes for balance rather than tugging and pulling on their mouths which is far more sensitive!
I remenber being told to grad the mane when jumping, or even to teach me to sit forward in gallop. Does no harm as far as I know, but I am happy to stand corrected if anyone really knows any different! I grab my horses mane when Im unsore of my balance...I remember doing hunter trials on my last horse and almost losing my balance because I had nothing to steady myself on (I'd hogged his mane)...wont be doing that again!
I also grab the mane and NOT the saddle when I am mounting/dismounting...simply because if the saddle were to slip, I wouldnt be pulled underneath the horse with it - instead, Ive got one arm holding the mane to keep me upright, and NEXT to the horse rather than underneath it, lol...besides that, it spreads my weight, so Im not twisting the horse's back as I pull myself up - some of the pressure is on the neck, and causes less damage....I dont like it when people mount my horse holding on to the saddle only - I see it as an accident waiting to happen!
p.s. I was watching Lucinda Green clinic (I think it was that - twas definately some professional XC and eventer anyway)...She was grabbing the horse's mane - infact, I dont think i saw many jumps where she didnt reach for the mane!