The behavior of the spin relaxation time of electrons bound to donors immersed in the middle of a CdTe quantum well was measured in the range of temperatures 10-80 K, by using picosecond pump-probe Kerr rotation. Different doping concentrations spanning from isolated donors up to a concentration beyond the metal-insulator transition were considered at a fixed magnetic field; at very low temperature, in insulating regime all electrons are bound to donors but for one high concentration we had to consider that a fraction of electrons is in conduction states. By increasing the temperature, the number of conduction electrons increases. The experimental temperature dependences were explained by invoking spin exchange between electron spins localized on donors and the spin of electrons promoted to conduction states. A good agreement between experiment and theory was found and allowed us to conclude that, while the spin of localized electrons undergoes the effect of both hyperfine and anisotropic exchange interactions, the D'yakonov-Perel' mechanism governs the spin relaxation of the conduction electrons for the whole range of the studied doping concentrations. Moreover, we identified the scattering mechanisms possibly undergone by the conduction electrons at low temperature.