The first thing to achieve in the downhill phase is to release the sacrolumbar joint; until you do that, going downhill is nothing more than the horse tiptoeing, taking short steps, and going really slowly or rushing onto the forehand to keep from falling on his nose. I will almost always try to achieve this release by finding a short, steep hill with fairly soft footing (see first photo) that is level at the top and level at the bottom with plenty of room for the horse to make a mistake.
I then bring the horse to the top of the "precipice", stop him, push him from behind so the back legs are well up underneath him and hold the front end in place with a soft but connecting rein (usually you don't have the hold the horse in front very much while doing this because the horse doesn't want to step off the precipice anyway.) After the horse's back legs are far enough underneath himself, I release the front end and let him take the first step forward, and then stop the horse again on the side of the hill, and push the horse's back legs underneath it again, then let it step forward again with the front legs, continuing with light (or heavier if necessary to keep the horse from charging down the hill) contact through the reins. By that time, because I have chosen a short hill for this, we are at the bottom, where I again stop the horse and push his hind legs underneath him. The natural inclination of the horse is to want to rush off because he is at the bottom and relieved to be there; this is the reason it is best to choose a hill with plenty of room at the bottom for making a mistake; however, you don't want to let the horse do this even if he wants to.
This exercise is almost guaranteed to release the sacrolumbar joint, but I almost always follow up by turning the horse around and making him go back up the same hill, and as long as you don't let the horse tow himself up the hill with his front legs or bound up the hill like a bunny rabbit, if the sacrolumbar joint wasn't released at the bottom of the hill, it will be by the time you get back to the top, as shown in the second photo. Bronte is a 17.1, 1,600 lb Thoroughbred-Shire cross so she required a lot of hand and a lot of leg to get her to do this the first time because holding all the weight up was tough for her.
After the horse gets the idea of this and can do it without having to be stopped between each step, I start using longer hills. When the horse can hold himself on his hindquarters at the walk going down steep hills, I start introducing trotting down slight grades (never any steeper than the horse can keep himself engaged while doing so). As the horse gets better at this, I lengthen these grades and steepen these grades.