Horses are all individuals. Some are more sensitive than others. One of the horses I ride jumps a mile if someone hits an adjacent horse (we ride Western, and sometimes people use the reins, which are long and not buckled together like the other sort - but only when we really need to, of course). The horse I have a part share in can be an awkward so and so. Using a whip, or a rein, makes not a blind bit of difference to her when she is in a strop. I ride in spurs - blunt ones, of course - and when she is in one of her moods, I touch her with those and she knows who is boss. There is no need to push them into her hard, and it's better than constant kicking for both her and me. Horses' skins are tougher than ours, and using a whip carefully - not beating the daylights out of them - doesn't hurt most horses nearly as much as it would hurt us. I'm sure they feel it (otherwise nobody would use a whip) but a sharp tap or two isn't that bad for most horses.