Horses can have horizontal lines on the hoof without having foundered. Some lines reflect a change in nutrition, fever, or an abrupt change in shoeing styles. A rule of thumb to determine if the rings reflect founder is to check if the space between the lines is significantly wider at the heels than at the toe. When the lines are closer together at the toe it means that the coffin bone has rotated and has pinched off the blood supply at the coronary band.
This will lead to a reduced growth rate. The blood supply at the heels is normal and the wider spacing reflects normal hoof growth. To truly determine if your horse has foundered I would definitely ask your veterinarian for radiographs of the feet. This is the only way to know for sure if your horse has rotation of the coffin bone.
