This is a good idea.
I'll share how I teach horses speed and cadence control on a loose rein; what I commonly refer to as 'teaching them to move with their brakes on'.
1: Make sure that the horse is far enough along in their training to be comfortable at all 3 gaits and has a decent stop.
2: Start out at the walk, either on the trail or in an arena, circles or lines, doesn't really matter. Walk for a few strides, stop, back them a few steps, then let them sit for a minute. Ask for the walk again.
3: Keep on repeating this until the horse is quick to stop and backs softly with their head down and breaking at the poll.
4: Then move up to the trot and repeat: trot, stop, back, sit, trot, stop, back, sit. This will help them learn to regulate their own speed and give them that nice easy jog.
5: Move up to the lope and repeat again. Consistency is key, every few strides you need to stop them and back them up.
6: Once they have started to get the idea and are becoming consistent about rating themselves, you can slow down on the teaching and move up to the correction stage. Just start stopping them and backing them up if they change their speed or raise their head.
7: This method is most effective if done for the last 10 or 15 minutes of every ride, when the horse's mind is most focused. Some catch on after just a few sessions and others needs quite a bit of time before they realize what you are trying to teach them. Most importantly, don't move up in gaits until they are consistent, soft, and smooth at the slower gait.
Not only wil this help them learn to control their own speed, but it will also teach them to stop on their butt, round into the bit at the stop, and stop hard. They will also generally start to have a more consistent level topline.