Snowfall is an essential component of the hydrological cycle, as it is involved in most precipitation on Earth, either directly as snow falling to the ground or indirectly as rain melted from snow. At the same time, the ice phase of clouds and precipitation is a key contributor to the Earth's radiative budget, making it a crucial aspect of climate-oriented research. Properly modeling snowfall for weather and climate applications requires knowledge of the "microphysics of snowfall", that is, a microscale description of snow particles and of the mechanisms by which they form and grow. Among different approaches to studying snowfall microphysics, remote sensing techniques and, in particular, meteorological radars, offer decisive insights. The interpretation of radar variables reveals information on the microphysical properties of hydrometeors over large spatial areas and in the vertical dimension. In addition to standard scalar variables, the Doppler spectrum measured by vertically-pointing radars allows separating the radar echo of hydrometeors as a function of their downward velocity. This discloses how radar signals are distributed between large, fast-falling, and small, slow-falling particles, and enables more refined analyses of snowfall. The goal of this thesis is to investigate snowfall microphysics by relying primarily on measurements from radars transmitting at different frequencies and on Doppler spectra. First, a multi-sensor dataset of in situ and remote sensing measurements of snowfall is presented, which was collected during the ICE GENESIS campaign in the Swiss Jura in January 2021. Methodological developments are then introduced, making use of cutting-edge machine-learning techniques to retrieve cloud and snowfall properties from remote sensing measurements. Specifically, one algorithm is developed to estimate the liquid water path, i.e., the integrated liquid water content in the atmospheric column, from radiometer brightness temperature. This quantification of atmospheric liquid water is of high relevance to snowfall studies, as microphysical processes are largely affected by mixed-phase conditions, wherein ice particles coexist with supercooled liquid water droplets. We then propose a novel framework to retrieve a number of snowfall microphysical descriptors from dual-frequency radar Doppler spectra, relying on a two-step physics-driven deep learning approach. In comparison with existing methods, this framework relaxes the need for certain prior assumptions on microphysical properties, or on perfect beam alignment and non-turbulent atmosphere. The retrieval is evaluated against in situ measurements from ICE GENESIS, and the encouraging -albeit not perfect- results pave the way for acute characterizations of snowfall properties on larger datasets. Finally, we focus on a specific snowfall event of ICE GENESIS. Through a detailed analysis of multi-frequency and Doppler spectral measurements, we propose interpretations of the complex signatures observed, which reveal the occurrence of distinct ice production and growth processes. Altogether, this thesis contributes to an improved characterization of snowfall microphysics through different perspectives, with (i) an open-access multi-sensor dataset of measurements in snowfall, (ii) new methodological tools to retrieve cloud and snowfall properties, (iii) a case study that underlines the relevance of radar measurements to improve our understanding of microphysical processes.