The Faraday effect is considerably enhanced in diluted magnetic semiconductor systems and can therefore be used as a sensitive tool to perform magnetic spectroscopy. We investigate the Faraday rotation of CdTe/CdMnTe superlattice systems with different barrier-layer thicknesses, which allow the study of dimensionality-dependent effects. By optically exciting the charge carriers and tuning the excitation wavelength we observe a step-like behavior at the absorption edge reflecting the electronic density of states and a strong excitonic resonance, which is much more strongly pronounced than in conventional spectroscopy like absorption or photoluminescence excitation. Temperature-dependent Faraday rotation measurements allow the observation of the phase transition from a paramagnetic state to a spin-glass state of the Mn 2+ spins. With decreasing barrier thickness LB we observe a strong deviation of the expected strength of the spin-exchange interaction below LB = 4 nm indicating a dimensional crossover to a two-dimensional spin system.