Always keep your eyes up when you are walking your course. See exactly what your horse will be seeing for the first time while under pressure, and think about how he might react.
"You can't teach someone to ride cross-country in one field, or even with constant instruction. It has to become a natural thing, and the only way to achieve that is to get out and do it." ~ Bruce Davidson
When you first begin to work on movements like shoulder in and haunches in, always start out with minimal angle and focus more on the quality of the bend.
Eventers need a saddle for cross country that allows them to move their center of gravity back for drop fences or anything on a downhill slope. Make sure your saddle has enough room for this to happen.
To be truly safe when jumping cross country, both horse and rider should learn to love that deep takeoff spot.
Please note that a "chip" is not the same as a deep spot. A chip is when the horse adds a stride unexpectedly, usually because the rider is going for a long spot or otherwise interfering with the horse's striding, and the horse is out of balance. And that's where the rotational falls happen. A deep spot in balance is the safest place to be.
For the cross country phase of Eventing, we need to be able to keep our horses balanced at the gallop while riding over rolling, undulating terrain. Yet it is becoming quite common these days for horses and riders to do most or even all of their jump training in a flat, perfectly manicured arena.
Make sure you do enough galloping and jumping training out on rolling hills if at all possible, to become adept at keeping your horse balanced at the gallop with the added challenge of varying terrain.
"Shoulder blades dropped into back pockets, lower rib cage softly lifted--buoyant and soft--open sternum, and breathing into lower back AND belly (to expand them) on the exhale." ~ Lee DiGangi
You can't make a horse relax. You have to HELP him relax. The mindset of helping rather than trying to make it happen makes a world of difference to the horse. This might sound like an obvious thing to say. But I see a lot of riders somewhat angrily trying to force their nervous and anxious horses to calm down and behave.
Be conscious of keeping your core engaged and your body stretched up tall as you soften the reins. Many riders mistakenly "let go" in their core and/or lean forward when softening the rein.
When preparing for a jump from a galloping position, one should always sink down into the heel before any touching of seat in the saddle, and only THEN should you take the mouth if necessary. Taking back on the reins first will almost always cause resistance.
"The basic techniques, or what they call basics, are more difficult than what comes later, this is the Trap of Dressage. Correct basics are more difficult than the piaffe and passage." ~ Conrad Schumacher
Horses brace against the bit when their RIDERS are bracing against their mouth. If you want your horse to soften, you need to be softer and more supple yourself.
Quote from Jimmy Wofford on the difference between being qualified to move up a level vs actually being READY to move up a level:
"Why not instead put the emphasis on how well you ride and how sweetly your horse goes for you, and lose this insane focus on climbing the qualification ladder?"
The best kind of "roundness" in Dressage comes when the exercises that you ride cause your horse to carry themselves properly, so that you are then able to simply allow them to become round, rather than trying to force it to happen.
"Many riders think dressage is just sitting trot, but I think the light seat can also be part of a dressage session. The light seat is a position that makes horses happy; it is a welfare position." ~ Christoph Hess
Because one hind foot is always in the air while at the trot, it is harder for a horse to refuse a jump from a trot approach vs a canter approach. So it can be a good idea to trot into a spooky fence that you think your horse might want to stop at. Just make sure you keep riding that trot until your horse is safely up in the air.
A good hand is the one that can smoothly resist or yield as necessary, and can quietly receive with precision the energy from the horse's hindquarters.
"At the sitting trot everyone wants to stop themselves from bouncing. What you have to do is let yourself go with the flow of the horse." ~ Charlotte Dujardin
"An engaged hind leg is the foundation that allows you to stretch the horse at a moment’s notice without him falling on his forehand." ~ Felicitas von Neumann-Cosel
"Concentrate on the transitions, forward and back, build the activity from behind. When you bring the horse slightly back, you still have to push her forward to the hand, you can keep riding as long as you can feel the hind legs in your hand." ~ Susanne Miesner
"The true joy for the good dressage rider is found in watching a horse develop mentally and physically through successful training." ~ Felicitas von Neumann-Cosel
"Never leave a resistant horse without reconciliation, even if you had to treat it very strictly on that particular day. Do not put it away until it obeys, but then a friendly relationship must be restored between trainer and horse. Always adhere to the principle: "The punishment is directed only at the disobedience, never at the horse"; as soon as the disobedience is over, it is our good horse." ~ E.F.Seidler
"True straightness can only be approached when managed in conjunction with the other elemental structures of riding in which it is inextricably housed: forward and calm." ~ Erik Herbermann
"Just as the sculptor at first chisels the future outlines of his work of art with powerful blows out of the crude block of stone, and then lets it develop in increasingly finer detail in all its beauty, the aids of the rider must also become more and more delicate in the course of the horse's education. Every rider should always keep this strictly in mind and especially avoid destroying with crude aids, out of impatience or other reasons, what he has built in his previous work." ~ Alois Podhajsky