Can you lengthen and shorten his stride on the flat? That's the key.
He's rushing, most likely, because he's unbalanced. Working on flat ground, make sure you can get three clear speeds of trot: a slow, sitting trot, an active, working trot and a lengthened trot (ask for this on a straightaway.)
When you feel like you've mastered this, find an area with a slight slope, and and ask for your shortened trot downhill and your lengthened trot uphill, with your active working trot in between. Practice the same exercise at the walk, and as an advanced exercise, at the canter.
Some horses learn to balance themselves up and downhill on their own after a period of time, others will require a little support from the rider no matter how familiar they are with the exercise.
This exercise should transfer readily to trail rides or hacking out; when you're approaching a downhill section; ask the horse to shorten stride and you should be able to stay in balance and in control down the hill.