A cold backed horse is a horse that bucks, flinches, or attempts to drop its back away when first mounted.
Traditionally, this was often assumed to be a habit. It's now known that it's often a symptom of soreness and/or of ill fitting tack (although it can become habitual in a horse that is not treated immediately, and it's not uncommon for the symptoms to persist for a few rides after treatment as the horse anticipates pain that no longer exists).
In some cases, especially in order horses, the symptom may reflect a tendency for muscular stiffness when first starting out. In this case, it's helpful to walk the horse out for a few minutes before mounting.