In-breeding is sometimes necessary amoungst certain limited breeds.
When you buy or breed a horse, often the owner will tell you the percent of line-breeding. Generally, there is often a low percentage for breeds such as friesians, cleveland bays, ect. The breeders want to maintain purebreds, and with horses being limited, line-breeding is often necessary. Fortuntely, an inbred percentage is normally under 5% for these types of horses.
However, I don't believe in line-breeding for popular breeds. I think it's quite silly to produce an in-bred horse when there is a large number of broods or studs to choose from - such as QH's. I think that it's counter productive. If you are breeding for the perfect horse, I think intelligence should be a factor as well. But of course, not all in-bred horses show in-bred characteristics.