The fastest way to make a horse stiff is to pull on both sides of a snaffle bit equally at the same time. This is why it is so important that you be able to ride a walk, trot, and canter confidently on a loose rein before you ever think about trying to achieve vertical flexion.
Once you have given up the reins for balance or control, you can begin to shape the horse's forward energy instead of stifle it.
A bit is a tool designed to supple the horse's body. A supple horse is one, which shows free play in all of its joints, starting in the head, neck, back, and loins and flowing down into the shoulder, hips, and legs. Supplying a horse starts with flexing his body laterally, stretching and loosening up the muscles which surround and control the joints.