So many misconceptions of what a half halt is!! A true half halt is what Anebel said, a re-belencing and re-grouping of the horse to prepare for the next movement, which of course requires the horse to be off the forehand and engaging the hind end to get through the next movement.
A bit of a tug on the mouth to slow the horse down is a beginners version of a steady. The half halt is far more complex than a simple tug back on the mouth. It involves all aids, leg, hand and seat used at the appropriate time in the horse's motion to give the horse the best chance of being able to re-balance himself. A true half halt is something a horse must learn, much like you would teach shoulder in or extensions. They do not just 'happen', initially the aids are further apart and occur over a longer time frame to give the horse the idea, so you may ask for the steady with the seat, then rein, and then put the leg on to get the re-balancing over the haunches. Eventually these aids, in the advanced horse, will appear to occur almost simultaneously and this is when the true half halt is coming into effect.
There are so many riders who are under the impression that the half halt is a very simple, tug of the rein and steady, but it is far from it. I'm not sure where the former notion comes from, whether it is from incorrect coaching, pony club or just basic ideas formed in ones own head, but riders need to understand that a half halt is far from a simple tug on the rein and is in fact quite a complicated series of aids used to achieve a specific goal.