Gandalf refers to Shadowfax in The Two Towers as the "Lord of all horses," and that's not just the wizard waxing lyrical about his favorite steed. Shadowfax is a direct descendant of Felaróf, the greatest horse to ever step hoof in Middle-earth. Both are members of the Mearas, a type of horse
far superior than the average.
Shadowfax is incredibly brave, loyal and smart, sticking by Gandalf even when charging into one of the greatest of battles and capable of understanding his every command. His finest attribute, however, is his speed. He's described as being "faster than the wind," which was proven when he carried Gandalf between The Shire and Rohan in under a week.