The nation-wide WSR-88D radar network is currently being upgraded for dual-polarized technology. While many convective, warm-season fuzzy-logic hydrometeor classification algorithms based on this new suite of radar variables and temperature have been refined, less progress has been made thus far in developing hydrometeor classification algorithms for winter precipitation. Unlike previous studies, the focus of this work is to exploit the discriminatory power of polarimetric variables to distinguish the most common precipitation types found in winter storms without the use of temperature as an additional variable. For the first time, detailed electromagnetic scattering of plates, dendrites, dry aggregated snowflakes, rain, freezing rain, and sleet are conducted at X-, C-, and S-band wavelengths. These physics-based results are used to determine the characteristic radar variable ranges associated with each precipitation type. A variable weighting system was also implemented in the algorithm's decision process to capitalize on the strengths of specific dual-polarimetric variables to discriminate between certain classes of hydrometeors, such as wet snow to indicate the melting layer. This algorithm was tested on observations during three different winter storms in Colorado and Oklahoma with the dual-wavelength X- and S-band CSU-CHILL, C-band OU-PRIME, and X-band CASA IP1 polarimetric radars. The algorithm showed success at all three frequencies, but was slightly more reliable at X-band because of the algorithm's strong dependence on specific differential phase. While plates were rarely distinguished from dendrites, the latter were satisfactorily differentiated from dry aggregated snowflakes and wet snow. Sleet and freezing rain could not be distinguished from rain or light rain based on polarimetric variables alone. However, high-resolution radar observations illustrated the refreezing process of raindrops into ice pellets, which has been documented before but not yet explained. Persistent, robust patterns of decreased correlation coefficient, enhanced differential reflectivity, and an inflection point around enhanced reflectivity occurred over the exact depth of the surface cold layer indicated by atmospheric soundings during times when sleet was reported at the surface. It is hypothesized that this refreezing signature is produced by a modulation of the drop size distribution such that smaller drops preferentially freeze into ice pellets first. The melting layer detection algorithm and fall speed spectra from vertically pointing radar also captured meaningful trends in the melting layer depth, height, and mean correlation coefficient during this transition from freezing rain to sleet at the surface. These findings demonstrate that this new radar-based winter hydrometeor classification algorithm is applicable for both research and operational sectors.