My objection to grabbing the saddle horn is that it's so close to your body it tends to lever you up and out of the saddle. Of course, the pommel of an English saddle is closer to ones body than the horn of a Western one. Better to grab the mane if you're going to be grabbing. When I'm jumping a strange horse or working with a green jumper I just get a handful of mane two strides out. But that's more to keep from nailing the horse in the mouth than to keep my balance. I've always discouraged grabbing as a general rule . . . if you sit down and back and keep your heels down, that's a better way to hang on.
I agree, especially mounting. The mane is going where the horse is.... the saddle may not ;~D