We report on growth by molecular beam epitaxy and magnetooptical investigations of digital alloys of diluted magnetic semiconductors. The digital alloys, i.e., very short-period superlattices, of interest here, were grown from nonmagnetic CdTe and magnetic Cd1-xMnxTe. In particular, quantum well structures containing the digital alloys in the regions of the quantum wells were fabricated. We searched for theoretically expected modifications of magnetic properties of digitally grown materials compared to those of random substitutional alloy counterparts, We monitored the magnetic behavior in our samples by studying their magnetooptical properties, We detected clear differences between magnetizations in random and digital alloys in samples grown along the [100] crystallographic direction. Unexpectedly, no modification of the spin-splitting (and, thus, of the magnetization) were observed in the case of digital quantum wells grown in the [120] crystallographic direction. On the other hand, exciton magnetic polaron binding energy in the latter structures was consistently greater by 10-20% than this quantity in similar samples grown along the [100] direction. The increase can be qualitatively understood in terms of the heavy hole mass anisotropy.