When you grab the front of the saddle, reach across to the other side of the pommel and grab it instead of the horn if you can. Then grab some mane hair and the reins with the front hand. You can pull pretty hard on the mane hair and it won't hurt them. I use it in dismounting too, just grab some hair
When you grab high on the horn your pulling harder toward you with the saddle. Its a physics thing I'm no good at explaining.
I will definitely try doing that!! Where do you grab with your back hand? Cause I usually just grab the back of the saddle to get on?