The temperature dependences of photoluminescence and exciton reflection spectra of the novel Cd_1-XDy_XTe diluted magnetic semiconductors (DMSs) were measured. The obtained experimental results reveal the magnetic polaron (MP) effect. This effect is observed for the localized, acceptor-bound excitons, and for the acceptor holes associated with Na or Li residual impurities. Simulation of the experimental data by a theoretical model allowed us to determine the characteristic energy of the MP as well as magnetic contributions associated with the average exchange field and the thermodynamic fluctuations of local magnetization for the acceptor-bound excitons and the acceptor holes. Furthermore, it was found that the values of the exchange interaction for the holes in Cd_1-XDy_XTe and Cd_1-XMn_XTe DMSs are close. These findings indicate that DMSs based on rare earth elements can be considered as novel promising materials for spintronics.