Your skill in riding determines if you can mount any particular steed. It is most often the case that powerful steeds need higher riding skill. Putting appropriate riding gear on the mount will help.

The ingame help reads:

Skill duration: random.
Type of skill : neutral skill.
Affecting stats: None.
It uses no endurance points.
While it is said the journey of a thousand miles begins with a single step,
there are many that would argue that it begins with finding the right horse.
Riding makes the trip faster and more comfortable, allowing you to go farther
with heavier gear and not arrive too exhausted to fight. While horses are
typically easy to manage, other, more exotic animals require more skill to
ride. Riding can be made easier with the use of certain types of gear.