If I had to point to one thing that made a huge difference in Clay's balance and strength this past year, it would probably be incorporating canter into our warm-up. Back in my hunter/jumper days, I had been taught that you walk and trot for ages before cantering, to get the horse's muscles ready for the more strenuous gait. But it turns out that the trot can in many ways be more strenuous than the canter, or at least, the canter works the body very differently, and therefor the trot doesn't really warm the horse up for the canter. In fact, the walk and the canter are more similar than the trot and the canter.
Here is a good explanation of what is happening in the horse's body at the trot and at the canter:
So, these days, I still start out at the walk and do a little trot (stretchy trot if he comes out steady and loose enough, which doesn't happen every time but we're getting there...) and then I get right into the canter, going around the whole arena several times each direction in a full medium canter/hand-gallop, in my half-seat, letting him have his head, keeping him very straight down the long-side with his poll the highest point.
It was rushy and unbalanced at first, but pretty quickly he started to have a nice rhythm and relax into it. As far as I go, I could canter like that all day!
Later in the ride when I ask for a more collected canter, for circles at the canter, and for some counter-canter, he feels SO MUCH more confident and comfortable with his foot-falls, balance and even with his breathing.
Another benefit of cantering like this in our warm-ups is that it sets the energy level for the whole ride and gets him thinking forward. Clay is not lazy by any means but he can lure me into over-using/nagging him with my leg aids on the days when he's feeling a little more quiet. I want to be able to ask him once for something and then for him not to change anything until I ask for something else, instead of every tenth step or so having to remind him "we're still doing that thing, keep going." Cantering around wakes him up mentally as well as physically.
If you're ready for it, start incorporating more canter into your warm-up. I think you'll be surprised to find your horse enjoys it, and in no time you'll notice a big difference in their overall endurance, balance, relaxation and strength.