Temperament
Your Horse's Temperament
Temperament does matter about your horse. On a scale from -10 to +10, temperament. The Lower a temperament, the less grumpy your horse will be. The Higher a temperament, the more likely your horse will buck you off.
A horse with a lower temperament, will make things a lot easier to train your horse's stats, because it will buck you off while riding much less frequently. A Horse with a high temperament, will make it more difficult to train your horse's stats, due to it oftenly bucking you off.
The only way to decrease a horse's temperament is by oftenly riding your horse, and pushing through all the times of being bucked off. Eventually, your horse's temperament would decrease.
But if you up to the challenge, go for a horse that has a high temperament.