Multi-frequency and Doppler spectral radars are valuable tools for retrieving information on the microphysics of precipitation, particularly snowfall. However, estimating microphysical properties from radar measurements is an ill-posed problem, i.e., different sets of solutions may correspond to the same radar observations. The uncertainty related to this ill-posedness is often difficult to quantify; furthermore, most retrievals usually rely on microphysical and scattering assumptions, whose impact on the retrieval is unknown. This work uses simulated radar measurements and the Markov chain Monte Carlo framework to retrieve microphysical information from triple-frequency Doppler spectra with minimal mathematical assumptions. Through this approach, we analyze posterior distributions retrieved from 10 representative examples of simulated measurements. Our results show that certain variables (e.g., effective diameter Deff) are well constrained, while others are more uncertain (e.g., shape parameter when a gamma particle size distribution (PSD) is assumed). We then use this framework to analyze the sensitivity of the retrieval to assumptions on atmospheric effects, microphysical properties, and scattering model. We find that the results are substantially impacted if an erroneous mass-size relation or PSD shape is used, with more than 50% increase in the 0.1–0.9 interquantile range of the Deff posterior distribution. We also investigate the case of bimodal Doppler spectra, where information regarding two hydrometeor populations is merged, and we quantify to what extent this information may be recovered depending on peak separation. This work sheds light on the information content of radar Doppler spectra, the sources of uncertainty, and the intrinsic limitations of radar-based microphysical retrievals.