Ruling out any medical issues first.
The answer is simple...you help him find his feet, by making him move his feet. A horse in the pasture, probably won't step over things voluntarily enough times to really benefit from it, so developing 'balance' under saddle, or in hand is up to you either way.
Trot poles, riding in the woods or on trails(going over and through anything 'safe enough' that you can think of and find), hill work, doing serpentines, and circle work, doing 'follow the rail' or 'cruising' type exercises (in which you ride in the arena, or round pen, with loose reins, and only focus on keeping the horse in the gait you desire...you don't interfere unless he breaks the gait; I tend to do alot of trot and canter of that exercise.
In your ground work, don't settle for lazy "if I have too" type work...get those feet moving there as well; your balance issues really start here, because if he's lazy on the ground, he will likely carry that to under saddle too; and it's more of a response to you not asking more of him, than him not knowing how to use his feet...Get her moving in the pasture with her pasture mates, I bet she doesn't trip quite as often there...simply because there is more motivation.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."