We report on optical studies of exciton magnetic polarons in CdTe/Cd1-xMnxTe quantum well structures with Mn contents 0.4 &le x &le 0.8. The magnetic polaron energies and formation times are measured by cw- and time-resolved photoluminescence under selective excitation. We find an overall increase of the polaron energy with increasing Mn-concentration in the whole range of Mn contents studied and attribute it to diffusion induced changes of the Mn profile at the interfaces between nonmagnetic and semimagnetic layers. In addition, we find that in these quantum structures the formation time of the polaron is predominantly determined by the Mn content and not by quantum confinement effects. The large band gap discontinuity (up to 1.2 eV) causes large splittings between heavy- and light-hole-states and leads to a strong anisotropy in the suppression of the magnetic polaron formation by magnetic fields applied parallel and perpendicular to the structure growth axis. For both orientations of magnetic field the polaron suppression is qualitatively described by model calculations.