Taking advantage of the recent developments in machine learning, we propose an approach to automatic winter hydrometeor classification based on utilization of convolutional neural networks (CNNs). We describe the development, implementation, and evaluation of a method and tool for classification of snowflakes based on geometric characteristics and riming degree, respectively, obtained using CNNs from high-resolution images by a Multi-Angle Snowflake Camera (MASC). These networks are optimal for image classification of winter precipitation particles due to their high accuracy, computational efficiency, automatic feature extraction, and application versatility. They require little initial preparation, enable the use of smaller training sets through transfer learning techniques, come with large supporting communities and a wealth of resources available, and can be applied and operated by nonexperts. We illustrate both the ease of implementation and the usefulness of operation the CNN architecture offers as a tool for researchers and practitioners utilizing in situ optical observational devices. A training dataset containing 1450 MASC images is developed primarily from two storm events in December 2014 and February 2015 in Greeley, Colorado, by visual inspection of recognizable snowflake geometries. Defined geometric classes are aggregate, columnar crystal, planar crystal, small particle, and graupel. The CNN trained on this dataset achieves a mean accuracy of 93.4% and displays excellent generalization (ability to classify new data). In addition, a separate training dataset is developed by sorting snowflakes into three classes and showcasing distinct degrees of riming. The CNN riming degree estimator yields promising initial results but would benefit from larger training sets.