A very good way of telling a lot about a horse is to ride a walk circle which incorporates a pole (or my personal preference, a plank, just in case they tread on it) on the floor, keeping your reins loose and doing as little as possible. Horses tell you a lot about their whole attitude to their life, work, and to jumping, and often about their experience, in their approach to a single pole/plank.
Some automatically lengthen their stride to and over it, others will march up then carefully add a shorter one if necessary. Some prefer to lead with one particular front leg and will shuffle to accomplish this. Some will tread on it or roll it the first time. If they do this repeatedly they’re probably not really cut out to be a jumping horse! Some concentrate on it, others are ‘away with the fairies’ and only notice it when they clout it. Some are suspicious, others blithe. Some just amble away after it, some jog, snatching the reins. It’s worth doing and then really thinking about what your horse is telling you, just in an exercise as simple as this one.
I first saw this in an Eric Smiley lecture/demo, he had all the riders just circling over a pole, and it was fascinating to watch how differently the horses coped with just that simple exercise.