Zero-dimensional excitons localized in CdTe/ZnTe nanostructures have been studied by spatially resolved magnetophotoluminescence spectroscopy. At zero magnetic field, exciton transitions present a doublet structure linearly polarized along two orthogonal directions. We attribute this doublet structure to bright exciton states \ +/- 1 > split by the local asymmetry of the localization potential. With increasing magnetic field oriented along the growth axis, a mixing of dark exciton states \ +/- 2 > and bright exciton states is observed for localization sites that present a large zero-field splitting. This allows a direct estimate of the electron and hole g-factors and of the isotropic exchange energy for strongly localized heavy-hole excitons.