The capability of current and future sensors to make accurate measurements of polarized microwave radiation allows for the investigation of particle shape and orientation. Additionally, the dichroic properties of media consisting of particles with preferential alignment will alter the polarization state of radiation emitted and reflected by the surface below a cloud boundary. Therefore, a deep understanding of the influence of particle orientation and shape upon radiation are required for remote sensing of both cloud and surface properties. In this study, we compute the scattering properties of three horizontally aligned snow crystals: two dendrites and an hexagonal plate. Additionally, we create two approximations using cylindrical plates. One uses a plate with a diameter equal to the maximum dimension of the respective snow crystal, utilizing an effective dielectric model which assumes the disk to be a matrix of ice with air inclusions. The other approximation uses a cylindrical plate of equal mass, with a radius chosen to conserve mass. To simplify the analysis, all particles have equal thickness. The results show a strong polarization response, particularly in the Q element of the Stokes vector. This polarization response is captured well by the two approximations. While the approximations are applicable for certain cases, there are discrepancies between the scattering properties of the idealized snow crystals and the two cylindrical plate models that may limit the generality of the approximations. Further radiative transfer studies are required to test the full applicability of the crystal approximations.