A Bayesian optimal estimation retrieval is used to determine probability density functions of snow microphysical parameters from ground-based observations taken during four snowfall events in southern Ontario, Canada. The retrieved variables include the parameters of power laws describing particle mass and horizontally projected area. The results reveal nontrivial correlations between mass and area parameters that were not apparent in prior studies. The observations provide information mainly about the mass coefficient a, somewhat less information about the mass exponent b and the projected area coefficient g, and minimal information about the projected area exponent s. The expected values for retrieved mass power-law parameters a 5 0.003 28 and b 5 2.25 are consistent with those from several prior studies that looked at the mass of aggregate-like particles and precipitating ice aloft as functions of maximum particle dimension. Differences from other studies appear related to differences in the dimensions used to define particle size. The retrieval allows the analysis of relatively large volumes of continuous observations, greatly enhancing sampling relative to single-particle analyses. The retrieved properties are used to constrain 94-GHz (W band) radar scattering properties for a variety of snow particle shapes. Synthetic reflectivities calculated using these scattering properties and observed particle size distributions show that a branched, spatial aggregate-like particle produces good agreement with coincident observed W-band reflectivities. Uncertainties in the synthetic reflectivities, estimated by applying a simple error-propagation model, are substantial and are dominated by the uncertainties in a and b.