A jump course set on the mildest of grades can seem much more challenging than the same course set on perfectly flat ground. Uphill lines require slightly more forward rides and downhill lines require more upper body control to maintain your horse's pace and balance. Turns on unlevel ground also require careful, precise balancing.
Mastering skills such as maintaining your horse's pace and balance will make you safer and more confident in many situations, such as trail riding and schooling in open pastures when you probably will encounter uneven terrain. In the show ring, it will help you smooth out the flow of your trips, giving you an advantage over other riders who haven't practiced riding on unlevel ground.
As an added benefit, working on a grade will strengthen your horse's muscles (particularly in his hindquarters) and improve his agility and coordination. Without even realizing that you're doing it, you'll be enhancing his jumping style and making him more adjustable and rideable.
Your primary job when riding on unlevel ground is to maintain your own balance well enough that you don't interfere with your horse. As your skills on hills advance, though, you'll be able to help him make minor adjustments so that every distance rides as smoothly as if you were on flat ground.
Riding a simple rectangle pattern on unlevel ground at the trot will teach you how to make adjustments with your aids and upper body, which will help your horse maintain his rhythm and pace without interfering with his balance.
In the photos here, I'm riding the pattern on Rachel Howell's Sin City ("Atti").
1. Going uphill, I'm posting to the trot with my upper body a few inches in front of the vertical. My legs are closed gently on Atti's sides to encourage him to maintain the same trot up the hill.
2. At the top of the hill, I prepare to turn Atti using balancing aids: I step into my outside stirrup, add a little more pressure with both legs and bring both hands toward my outside hip to help balance him. I'll maintain a steady pace across the hill and then.
3. .prepare for the turn down the hill by using the same balancing aids. In another stride, I'll also bend my elbows and raise my inside hand a little as I move it toward my outside hip to tell Atti to slow down. Then I'll use my outside aids to straighten him off the turn.
4. Traveling downhill, I bring my upper body back--compare my position here to the more forward position I have in Photo 1. I'll keep my shoulders balanced over my hips all the way down the hill and keep my legs closed on his sides to bring him into the bridle.
To learn how I ride the exercise at the canter and how I apply these skills to jumping up and down hill, see "Survive the Slant" in Practical Horseman's February 2010 issue.