Instructions
Look in the auctions for any players selling a Croesus. These events are rare, but they do occur on occasion. However, keep in mind that these horses are incredibly rare and will cost an enormous amount of equus (in-game money). Some have sold for upwards of 4 million equus. It's pricey, but it's also the least time-consuming way to get a Croesus.
Ask another player to make a trade. If you're short on funds, but you have another horse (preferably a rare Divine horse) that you no longer want, check the player database for players that might have a Croesus. You could also contact players that are selling a Croesus in the auctions. If you're lucky, they might be willing to cut a deal with you.
Name one of your horses "Junior Croesus." On the 13th of every month, one horse in the game that is named Junior Croesus will be transformed into the real Croesus. There is a debate over whether naming multiple horses "Junior Croesus" will increase your chances of getting one, but in any case, it's usually best to bestow the name on horses that you haven't leveled up very much. This is because the Junior Croesus' skills will become 470 if it turns into a Croesus. For some horses, this is actually a severe drop that could undo months of training.
Be extremely patient. This might be self-evident, but any of the methods above will likely take a long time to come to fruition. Less than 0.001 percent of the game's population have this horse, and it's very rare for a player to want to part with their Croesus. Also, with 6 million players in the running, your monthly chances of transforming a Junior Croesus into a Croesus are roughly equivalent to your chances of winning the lottery. It's not impossible, but it can take a very long time, and you have to exercise extreme patience if you want this incredibly rare horse.