Some Saddlebred horses do have significant sway backs. Currently, this is believed to be the result of a genetic influence. The “sway back” gene is believed to be a recessive gene, meaning that both the dam and the sire must be carriers to create an affected foal.
These low-backed horses do not appear to demonstrate painfulness associated with the condition and some have even gone on to be successful show horses.
However, pathology reports on affected horses do suggest that there can be varying degrees of damage to the spinal cord and the ligaments that support the spinal column on a case-by-case basis. For these reasons, the breed association does not encourage breeders to perpetuate this trait. Typically these horses are not painful and yes, they can be ridden, providing they are sound.