A new method to automatically classify solid hydrometeors based on Multi-Angle Snowflake Camera (MASC) images is presented. For each individual image, the method relies on the calculation of a set of geometric and texture-based descriptors to simultaneously identify the hydrometeor type (among six predefined classes), estimate the degree of riming and detect melting snow. The classification tasks are achieved by means of a regularized multinomial logistic regression (MLR) model trained over more than 3000 MASC images manually labeled by visual inspection. In a second step, the probabilistic information provided by the MLR is weighed on the three stereoscopic views of the MASC in order to assign a unique label to each hydrometeor. The accuracy and robustness of the proposed algorithm is evaluated on data collected in the Swiss Alps and in Antarctica. The algorithm achieves high performance, with a hydrometeor-type classification accuracy and Heidke skill score of 95% and 0.93, respectively. The degree of riming is evaluated by introducing a riming index ranging between zero (no riming) and one (graupel) and characterized by a probable error of 5.5 %. A validation study is conducted through a comparison with an existing classification method based on two-dimensional video disdrometer (2DVD) data and shows that the two methods are consistent.