We study the polarization dynamics of exciton-polaritons propagating in sub-mm-thick (Cd,Zn)Te bulk crystals using polarimetric time-of-flight techniques. The application of a magnetic field in Faraday geometry leads to synchronous temporal oscillations of all Stokes parameters of an initially linearly or circularly polarized, spectrally broad optical pulse of 150-fs duration propagating through the crystal. Strong dispersion for photon energies close to the exciton resonance leads to stretching of the optical pulse to a duration of 200-300 ps and enhancement of magneto-optical effects such as the Faraday rotation and the nonreciprocal birefringence. The oscillation frequency of the exciton-polariton polarization increases with magnetic field B, reaching 10 GHz at B∼5 T. Surprisingly, the relative contributions of Faraday rotation and nonreciprocal birefringence undergo strong changes with photon energy, which is attributed to a nontrivial spectral dependence of Faraday rotation in the vicinity of the exciton resonance. This leads to polarization nutation of the transmitted optical pulse in the time domain. The results are well explained by a model that accounts for Faraday rotation and magnetospatial dispersion in zinc-blende crystals. We evaluate the exciton g factor |g _exc|=0.2 and the magnetospatial constant |V|=5×10^-12 eV cm T^-1.