Albegas: President Bios is the second President of the Dellinger Empire, and rides a stallion.
Black Butler: Ciel Phantomhive is from a wealthy English family. He rides horses when going to hunt at his state.
Youichiro Kanzaki from Cardfight!! Vanguard G is a Sharp-Dressed Man who is shown in a scene to own a large property with at least one butler and an unspecified number of horses; his two favourites are Herrshaft and Ehrgeiz.
Cesare - Il Creatore che ha distrutto takes place in 1491-92, well before the invention of other modes of transportation, but even then most people did not own horses. Cesare Borgia comes from one of the richest families around. He not only has a lot of horses, he's very skilled and knowledgable with them. Scholarship Student Angelo, on the other hand, has very little experience riding, and in the first chapter, the two protagonists meet when Cesare saves Angelo from a Moody Mount. In the end of the manga, Cesare is training horses for a horse race, which he wins right around the day his father was elected Pope.
Lelouch Lamperouge of Code Geass is actually a member of the equestrian club in Ashford Academy, according to Rolo. However, it was rarely emphasized much throughout the show due to how viewers see him as being out of shape. Though there are a few scenes where he rides a horse such as the opening of R2.
Daimos: Richter is an Alien Prince and he knows how to ride a horse, as seen by his flashback duelling Aizam.
Daltanious: In Dolmen's flashback, Emperor Palmillion, in his youth, rode horses. Upon falling over and injuring himself, his clone was tortured to receive the exact same injury.
Fukiko "Miya-sama" Ichinomiya from Dear Brother is in the equestrian club at school, and fittingly, she's also from a very wealthy family.
Destiny of the Shrine Maiden: Chikane is a wealthy Ojou who is trained in horseback riding and has a horse named Saint Just.
Entaku No Kishi Monogatari Moero Arthur: King Arthur rides a white Pegasus into battle (despite the fact that in the original myth, there wasn't one).
The Familiar of Zero: Louise is the daughter of an aristocratic family and horseback riding is listed as her special skill.
Four Knights of the Apocalypse: Anne. Since her father is a feudal lord, she has been raised as a rich lady. When traveling with her friends, she rides on her horse Sylvan, who she calls her best friend.
Early in Gundam Wing, Relena's school is shown to have a horse riding class. It's meant as a visual aid of how ritzy the school is and underscore that Relena herself is a Lonely Rich Kid.
Hello! Sandybell: As a display of Kitty Shearer's immense wealth, she rides her horse all over Scotland, and it's mentioned that her father pays for her horse-riding lessons. And this is despite owning her own personal limousine and stylish Cool Car.
Isabelle of Paris: The Laustins travel through horse pulled carriages, and Isabelle knows how to ride horses on her own. Justified since this is 18th-century France.
KiraKira★Pretty Cure à la Mode: Ciel is the number one patissier in France, and all her sweets shop , redgardless of country, are always filled with people. She rides a Pegasus, and her Animal Motif is one too.
Lady!!: Saint Patrick's school is an academy for young girls from the British Elite. Amongst the students are Vivian Spencer, the School Idol who's beautiful, glamorous and from a rich family. She is an expert horse-rider and owns multiple horses, one of which was given to the protagonist Lynn, and public opinion has it that she'll represent the school at the Olympics and win the Lady's Crest award.
La Seine No Hoshi: Justified, since this is 1780s France. Robert (the firstborn son of the noble de Forges family) gives Simone her signature White Stallion, and the nobles all travel by horse carriage.
Love Live!: One of Mari Ohara's hobbies is horse riding. In Dengeki stories, Mari is sometimes depicted with her horse, Starbright.
Mari: The horse I get along best with since I was a child is Starbright! A thoroughbred horse with a large build, it has a pattern on its forehead that resembles a cool white star. It's tall so riding it is a bit hard, and its temper is also a bit rough, but it's clever and kind only to me, a real tsundere horse♡ And oh, it's female, by the way. It's my best friend!
Ayaka of Negima! Magister Negi Magi is a super wealthyOjou who is trained in riding horses - she's in the equestrian club at school and at her house they own a stable of horses she often rides for fun.
Cavendish from One Piece, is hardly ever seen without his steed Farul and he always acts upper-class before a side story reveals he used to be outright royalty before he was deposed.
Princess Connect! Re:Dive: Rei is from a family of wealthy nobles. She teaches Yuuki how to ride a horse in one of her character episodes while she rides her own, named "Marengo".
The Rose of Versailles: Oscar is from a noble French family and was educated in fencing and horseback riding by her father.
The title character from Saber Rider and the Star Sheriffs is British, and comes from a wealthy family. He also rides a robotic horse in to battle.
Voltes V: Prince Heinel is a Horned Boazanian, meaning he's from the elite class, that directly oppress the Hornless Boazanians and enslave them. He has a white horse of his own, and rides it into battle in the Grand Finale after the slave rebellion was successful and the nobles have fled en masse.
The World God Only Knows: According to Mio's profile, horseback riding was one of her favorite hobbies back when she was rich.
