I like to think I have a fairly decent handle on the lore, but always enjoy seeing how older editions do thing. (Came into the game with 4e)
Well since I was a Unicorn player in the card game I grabbed some of the older Unicorn books (way and secret) just to get more of a background and history about them. Which is nice as even with newer editions you have a continuity of events.
A brief background of the Horiuchi and Horiuchi Shem-Zhe:
The Horiuchi are one of the most unique families of all the great clans in that they are composed of descendants of many Clans and not just the Unicorn. Their founder, Horiuchi Shoan, born of the Iuchi family and given the honorary title of Hori or moat for an incident where she protected the former Unicorn Clan Champions two children, one of who was Shinjo Shono, the current damiyo of the Shinjo family. She did so through the Castle of Water spell maintaining it until bushi (warriors) could come and kill the bandits trying to harm her charges. Originally she was to be the only Horiuchi, a special title that would die with her. However the Clan Wars occurred in which the Great Clans fought at first until the true enemy, Fu Leng emerged and the Clans united to put him down. This was also the war that ended the Hantei dynasty thanks to Fu Leng killing the last Emperor of the Hantei. From this war numerous orphans came about and Shoan was the one that sought out and took care of them. Amongst those orphans was Moto Shem-Zhe. He, along with his brothers were adopted by Shoan and took on the name of the Horiuchi.
For the Horiuchi they take on the orphans of the Empire, raise them, and train them. When they come of age they are given a choice- they can become a Horiuchi, return to their Family or become a ronin. Those that become Horiuchi in turn will travel the Empire looking for the unwanted orphans and bring them back to be raised. Because of this you can find children from families of all the Clan that are either currently being raised or have become Horiuchi, at the same time it is the smallest of the Unicorn families and the least martial. An example of this is Junichiro, born of the Isawa family and adopted by Shoan after becoming an orphan he chose to take on the name of the Horiuchi and wandered the Empire finding other orphans until he was killed.
Horiuchi Shem-Zhe is the second damiyo of Horiuchi family, taking the mantle from Horiuchi Shoan who is now dead. Different from many samurai, he does not seek to raise the status of his Family, instead seeks to continue the work of Shoan while also establishing a role for the Horiuhci. As one of the top Shugenja of the Unicorn, Shem-Zhe has worked on several projects for Moto Chagatai, Khan and Champion of the Unicorn in addition to his responsibilities in running the Family and caring for orphans.
A quick word on Unicorn magic. While they have the same spells as the other Clans thanks to their long journey into the wider world they have learned Gajin magic (though they disguise these as normal spells) and as such have access to many unique spells and abilities. They also have Meishodo or name magic. This was learned by Iuchi himself (all of the main families are named for an ancestor that worked along side the Kami of the Clan with the Clan of the Champions named for the Kami themselves, except the Unicorn, for who Shinjo was the Kami but she later striped the Shinjo family of championship and passed it onto the Moto Family, oh and the Moto family is for the Moto tribe that they met outside of Rokugan (the Empire) and who joined the Unicorn clan, so yes the Moto are part gajin). Meishodo is a powerful form of casting that is much quicker than normal magic, however it lacks the flexibility of normal magic and for a long time a Shugenja would have to chose one to pursue, as those that cast Meishodo could not cast normal magic and visa-versa. The Horiuchi family however discovered a way around this limitation however that knowledge has been kept for the Unicorn only. Also to my knowledge Meishodo is only practiced by the Unicorn Clan as well.
For schools Unicorn favor Air and Water spells, speed, movement and support.