Hobdaying is when a strip of muscle is removed from just below the larynx. Usulaly done when there is paralysis in the flaps on top of the larynx. The scar tissue then supports the larynx.
Is probably the oldest wind op (apart from tubing) and is rarely done by itself nowadays. When a horse receives a tie-back they usually hobday to help support it.
The new craze is for tie-forwards. Being an inside out tie-back there is not any need seen for it to be supported.
People are going for the tie forwards as there is only a 3 week recovery. With a hobday there is an open wound and 6 weeks is needed.