Model polar clusters of Stockmayer (Lennard-Jones + point dipole) particles exhibit spontaneous breaking of orientational symmetry in a wide range of temperatures. The form of the orientational anisotropy best accommodates the tendency of polar particles to form chains of dipoles in head-to-tail arrangement. It persists through temperatures characteristic of solid-liquid coexistence for dipole strength mu*(2) = mu(2)/epsilon(3) = 1, and to about twice the range of solid-liquid coexistence temperatures for mu*(2) = 3. These studies extend earlier work [H. B. Lavender, K. A. Iyer, and S. J. Singer, J. Chem. Phys. 101, 7856 (1994)] in which orientational order parameters for clusters are defined and the global orientational order was observed for much smaller clusters. In this work we also study orientational order with respect to the cluster Liquid-vapor interface and find significant disagreement with density functional theory predictions.