Low-temperature polarized and time-resolved photoluminescence spectroscopy in high magnetic fields (up to 30 T) has been used to study the spin-polarization, spin-relaxation, and radiative lifetimes of excitons in wurtzite semiconductor (e.g., CdSe) colloidal nanocrystals. The applied magnetic field leads to a significant degree of circular polarization of the exciton photoluminescence, accompanied by a reduction in the photoluminescence decay time. The circular polarization arises from the Zeeman splitting of exciton levels, whereas lifetime reduction results from a polarization-preserving field-induced mixing of exciton levels. We analyze these experimental findings in terms of a simple model that combines both Zeeman effect and exciton-level mixing, as a function of the relative orientation of the nanocrystal c-axis and the magnetic field. This model is able to simultaneously describe the degree of circular polarization and lifetime reduction of the exciton photoluminescence, permitting us to quantify the exciton, electron, and hole g-factors.