By foot: Horses were often led or ridden from one place to another. This was common for short distances, or when only a few horses needed to be moved.
By ship: Horses were often transported by ship, especially for long distances or across bodies of water. Ships specifically designed for transporting horses, called horse transports, were used for this purpose.
By train: Horses could also be transported by train, in special railroad cars called livestock cars or horse cars. These cars were designed to provide enough space and ventilation for the horses, and often had features such as stanchions or stalls to keep the horses in place.
By wagon or cart: Horses could also be transported in wagons or carts, often pulled by other horses or by oxen. This was common for local travel or for moving a small number of horses.
Horse-drawn vehicles: In some cases, horses themselves were used to pull specialized horse-drawn vehicles designed for transporting other horses. These vehicles might be used for short distances or for moving larger numbers of horses.