The qualities of conformation and movement determine what a horse is capable of, while temperament and rideability decide whether you will enjoy doing it; for an amateur buyer these two factors are more important than any others, even though almost no advertisement highlights them because these characteristics cannot be photographed.
The horse’s temperament refers to its character: whether it is brave or shy, hot or steady, generous or bossy. Rideability is more specific and concerns the ride itself: how readily the horse takes in your cues, how it reacts when you make a slight mistake, and whether it continues to try. A horse might be a saint when on the ground but difficult to ride, or on the contrary it may be excellent on the ground yet a hardship to ride, so you should keep an eye on both aspects.
There is no one temperament that is correct, only one that suits you. A horse that is very sensitive reacts to the slightest aid, something that a professional values but which a nervous beginner finds tiring. A more steady horse tolerates your errors and requires clearer and stronger aids in order to start moving. In neither case is one superior. What is important is the match, which is why the honest self-evaluation when choosing the right dressage horse can be found here is the most important page you will prepare.
If you observe a horse rather than talking to it, you can get a good idea of its temperament before it has been ridden at all. Consider how it behaves in the stable, when it is caught, when it is being tied up and when its feet are handled. Also note its reaction to new things, such as a jacket on the fence or a dog walking by. What’s interesting isn’t whether the horse reacts, since any horse could do that, but rather how quickly it returns to calmness. A horse which notices something and then calms down has a sound mind. A horse which cannot get back to calm is giving you a message that you should pay attention to.
The most revealing situation when riding is making a deliberate small error—sitting a bit too heavily, giving an incorrect aid, or asking for a transition in a poor way. The horse that is easygoing just ignores it, while the more difficult one keeps the mistake in mind. This one test tells more to a beginner than any amount of smooth trotting.
Ask the direct questions, including those which may seem impolite. Is it acceptable to load the horse, to clip it, to shoe it, or to hack it alone? Has it ever reared or bolted? Is it taking any calming supplements or medication? Those who sell good horses give straightforward answers. Evading the questions is in itself an answer. Whatever you are told, make sure the key points are put in writing in the contract later so that a verbal reassurance can be relied upon.