At the lower levels, always approach a drop on a loose rein. Do not hold onto the horse’s face; restricting the neck is what causes horses to leap out and “swan dive.” I teach my baby horses to pop down small banks on the longest, loosest rein possible. Let them put their heads down and SEE the edge of the drop. A horse with its head down will rarely launch off the edge, but instead fold their hocks and step down gently. Of course green horses will make mistakes, hesitate, dance, and still may leap off anyway; but the more times you approach with a soft loose rein, they will learn to relax and drop down with confidence.
On a greenie, I approach a drop at a walk or slow sitting trot; my feet forward, hands low and wide with long reins, eyes up, soft lower back in a “C” position to absorb an awkward landing. Let the horse jump down away from you, don’t try to keep up with the motion or you’ll inevitably end up ahead of them (causing imbalance, rough landing, popping up the neck, or a stop). Open your fingers and let the reins slip so the horse feels no restriction on his face (and so he doesn’t pull you over his head…BTDT!).
Schooling first drop on a 3yo.