The purpose of the free walk is to show good relaxation and ground cover. To me the non specificity of the test as to whether the free walk is on a long or loose rein means they the rider needs only to ride the movement as to best show the free walk.
When schooling you must not let the horse jerk the reins out of your grip. Let the reins go very incrementally and maintain the contact. It is useful if the horse is used to the whip to give a tap when the horse jerks the reins, and remember to continue riding throughout the movement with your leg and seat to keep the walk active and reaching for the contact. For now, keep the horse on a contact with long reins. As she learns to be more responsive to you in the free walk, the reins can be longer.
The free walk is a physical break for the horse, not a mental time out to lala land. Keep this in mind.
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