We applied the Numerical Maxwell Model of three-dimensional simulations (NMM3D) in the Dense Media Radiative Theory (DMRT) to calculate backscattering coefficients. The particles' positions are computer-generated and the subsequent Foldy-Lax equations solved numerically. The phase matrix in NMM3D has significant cross-polarization, particularly when the particles are densely packed. The NMM3D model is combined with DMRT in calculating the microwave scattering by dry snow. The NMM3D/DMRT equations are solved by an iterative solution up to the second order in the case of small to moderate optical thickness. The numerical results of NMM3D/DMRT are illustrated and compared with QCA/DMRT. The QCA/DMRT and NMM3D/DMRT results are also applied to compare with data from two specific datasets from the second Cold Land Processes Experiment (CLPX II) in Alaska and Colorado. The data are obtained at the Ku-band (13.95 GHz) observations using airborne imaging polarimetric scatterometer (POLSCAT). It is shown that the model predictions agree with the field measurements for both co-polarization and cross-polarization. For the Alaska region, the average snow depth and snow density are used as the inputs for DMRT. The grain size, selected from within the range of the ground measurements, is used as a best-fit parameter within the range. For the Colorado region, we use the Variable Infiltration Capacity Model (VIC) to obtain the input snow profiles for NMM3D/DMRT.