This paper addresses the challenge of vine pruning, a crucial and laborious task in agriculture, using robotic technologies and vision based feedback control. The complex structure of vines makes visual servoing difficult due to challenges in 3D pose estimation and feature extraction. A novel approach to vision based vine pruning is proposed, based on the combination of Iterative Closest Point (ICP) point-cloud alignment and position-based visual servoing (PBVS). Four ICP variants are compared within PBVS in vine pruning scenarios: standard ICP, Levenberg-Marquardt ICP, Point-to-Plane ICP, and Symmetric ICP. The methodology includes a dedicated ICP initial guess to improve alignment speed and accuracy, as well as a procedure for generating reference point clouds at pruning locations. Live experiments were conducted on a Franka Emika manipulator equipped with a stereo camera, involving three real vines under laboratory conditions.