Sword and Fan does offer a lot of military background for Rokugan. Including the following excerpt:
Light cavalry is a staple of any Rokugani army, even if it otherwise has little in the way of mounted warriors. 
This implies each and every clan has cavalry. For most clans, they even give a renowned unit name. But the only clan that actually has any cavalry school in the core book is of course unicorn with both their Moto and Utaku schools . The rest of the chapter contains cavalry unit names and descriptions, but the Table of contents does not indicate there are any new schools included.
This leads to the question:
Where are the rules for those schools, paths, or alternate schools that are dedicated cavalry and not from clan unicorn?
1 - Sword & Fan, p.72
2 - L5R 4E Core, p.130 & p.132