The results of a detailed and systematic study of time-dependent, space-dependent, and steady-state neutron spectra in different assemblies of various H2O-D2O mixtures in the temperature range of 253 to 21 K are reported. By the matrix diagonalization method, the multigroup Boltzmann diffusion equation was solved to obtain asymptotic and transient spectra in assemblies at 253 K, with buckling values ranging from 0 to 0.4 cm−2. Mixtures with D2O content of 20, 50, and 80 wt% are considered. The calculated values of the fundamental mode decay constant and the diffusion parameters are compared with the experimental values reported by Salaita and Robeson. The multigroup time-independent source-free Boltzmann equation was also diagonalized to obtain spatial eigenvalues and eigenfunctions. By using these eigenfunctions, neutron spectra and the effective diffusion length L(x), at different distances from the source plane, were calculated at 253 K. The asymptotic values of L(x) compare fairly well with those calculated by using the measured values of D0 and in mixtures with a D2O content of 20, 50, and 80%. For the steady-state problem, the multigroup inhomogeneous Boltzmann diffusion equation was solved by the matrix inversion method for assemblies at 77 and 21 K with buckling values ranging from 0 to 0.1113 cm-2. Mixtures with D20 content of 0, 5, 10, 20, ... 90, 95, and 100% are considered. At 21 K, the relative usefulness of different assemblies as cold-neutron sources is discussed. For some selected assembly sizes, we determined the optimum H2O-D2O mixtures that would give maximum cold-neutron flux. The optimum mixtures for buckling values of 0.1113, 0.0158, and 0.001 cm-2 are those with nearly 30, 70, and 90% D2O, respectively; the corresponding gain factors for graphite-filtered neutrons are 1.85, 4.17, and 13.57, respectively. We find that in mixtures, as in the cases of H2O and D2O ice, cooling an assembly below 21 K does not decrease the effective temperature of the neutron distribution below that obtained at 21 K.