Answer

By Your Horse

Dressage rider and instructor Claire Lilley says…

I was always taught to have my whip on the off-side (right) of the horse’s withers when mounting so that it doesn’t get in the way when you mount. The other advantage is that if some kind person is giving you a leg up, you don’t accidentally poke them in the eye with it!
When riding in a group or in an exam situation, it’s usual to carry your whip on the inside so you don’t catch another rider’s horse. When schooling your horse on your own, you may sometimes need your whip in your outside hand, for example to reinforce your outside leg aid when asking for canter. Your whip should never be used in punishment or anger. Whether it’s short or long, it should be used as an extra leg aid when required.