But once the basics are there, the mule can be put into a hackamore. Review the basics you taught with the snaffle and establish the control with the hackamore with light pulls and releases. Building confidence in the mule and teaching the lessons thoroughly will make him trustworthy in the hackamore. The Hackamore is poor stopper in the beginning, so teach this in the snaffle and establish it before putting the mule into the hackamore. It's not safe on a green mule who might have the tendency to run away.
Runaways require doubling, and that is best accomplished with a snaffle.
It is only a fair device to teach backing and neck reining. Since it does not work well with a steady pull, it is not the best equipment to teach the mule to stay at a steady speed. It takes some initial training before it can be used on the mule and it takes a lot of time and patience to teach the mule to work in it. Some mules who have already been harshly bitted or had the chain used severely on the nose may not be good candidates for Hackamore training. It is best to use on a mule that has been trained to be light and responsive with a great deal of time spent on the basics.