Due to the competition between spatial and magnetic confinement, the density of states of a quasi two-dimensional system deviates from the ideal step-like form both quantitatively and qualitatively. We study how this affects the spin-subband populations and the spin-polarization as functions of the temperature, $T$, and the in-plane magnetic field, $B$, for narrow to wide dilute-magnetic-semiconductor quantum wells. We focus on the quantum well width, the magnitude of the spin-spin exchange interaction, and the sheet carrier concentration dependence. We look for ranges where the system is completely spin-polarized. Increasing $T$, the carrier spin-splitting, $U_{oσ}$, decreases, while increasing $B$, $U_{oσ}$ increases. Moreover, due to the density of states modification, all energetically higher subbands become gradually depopulated. ; Comment: 3 pages, 3 figures