We have calculated cross sections for vibrational quenching in collisions of O-17(2)(X (3)Sigma(g)(-)) with He-3 at cold and ultracold temperatures, explicitly accounting for the electronic spin degree of freedom. The observed population of the final spin-rotational levels can be interpreted on the basis of useful "propensity rules" governing the intensity of the collision-induced transitions. In addition, it is found that the orientation of the molecular spin is reasonably robust against collisional relaxation, even in vibrationally excited states. This finding implies that magnetic trapping of vibrationally excited, but rotationally and translationally cold, molecules may be possible. (C) 2003 American Institute of Physics.