'Rhinoplasty' is a general term for surgery involving the nose. The actual procedures done vary greatly depending on what is needed and the surgeon doing it.
I think what you're referring to is a stiff nose that doesn't bend as much when it is touched. This would happen if cartilage grafts that are stiffer than your actual nose (eg. rib grafts) are used. If ear cartilage or septal cartilage are used, your nose will still feel quite natural.
Hope this helps.