Usually hydrologists talk of "precipitation" and are quite reticent to talk about its phase. This is because it is not easy to separate the snowfall and rainfall. In simple approaches, temperature alone is chosen as separator since ACOE (1956). However, temperature alone is not enough. As they say well Harder and Pomeroy (GS), 2014, and Ye (RG) et al., 2013. However, we still stick with the only temperature for practical purposes, and because other solutions are unfeasible (missing data, tools or time to go deeply) or not so important. The core of this methods is to identify a threshold temperature over which precipitation is rain and above which precipitation is snow. Most of the time the two temperature (below and above which) are not the same. So we better talk of temperature thresholds.
Besides, researchers agree that these thresholds can vary from location to location, due to several meteorological and terrain factors.
A promising method that can potentially be used for making temperature thresholds variable in space in connection with the use of satellite data is proposed in the paper by Abera et al., 2015.
Waiting for it to be available, please find below a collection of papers on the topic. They, obviously contain further references.
ACOE, US Army Corps of Engineers. 1956. Snow Hydrology: Summary Report of the Snow Investigations. North Pacific Division; Portland, OR, 437.
AuerAH. 1974. The rain versus snow threshold temperatures. Weatherwise 27: 67.
Dai, A., 2008: Temperature and pressure dependence of the rain- snow phase transition over land and ocean. Geophys. Res. Lett., 35, L12802, doi:10.1029/2008GL033295.
Feiccabrino, J., & Lundberg, A. (2009). Precipitation Phase Discrimination in Sweden (pp. 1–16). Presented at the the 65th Eastern Snow Conference, 2008
Harder P, Pomeroy JW. 2013. Estimating precipitation phase using a psychrometric energy balance method. Hydrological Processes. DOI: 10.1002/hyp.9799
Harder, P., & Pomeroy, J. W. (2014). Hydrological model uncertainty due to precipitation-phase partitioning methods. Hydrological Processes, 28(14), 4311–4327. http://doi.org/10.1002/hyp.10214
Harpold, A. A., Kaplan, M. L., Klos, P. Z., Link, T., McNamara, J. P., Rajagopal, S., Schumer, R., and Steele, C. M.: Rain or snow: hydrologic processes, observations, prediction, and research needs, Hydrol. Earth Syst. Sci., 21, 1-22, doi:10.5194/hess-21-1-2017, 2017
Kavetski, D., Kuczera, G., & Franks, S. W. (2006). Calibration of conceptual hydrological models revisited: 1. Overcoming numerical artefacts. Journal of Hydrology, 320(1-2), 173–186. http://doi.org/10.1016/j.jhydrol.2005.07.012
Kienzle, S. W. (2008). A new temperature based method to separate rain and snow. Hydrological Processes, 22(26), 5067–5085. http://doi.org/10.1002/hyp.7131
Matsuo, T., Y. Sasyo, and Y. Sato, 1981: Relationship between types of precipitation on the ground and surface meteorological elements. J. Meteor. Soc. Japan, 59, 462–476.
Motoyama, H., 1990: Simulation of seasonal snow cover based on air temperature and precipitation. J. Appl. Meteor., 29, 1104– 1110.
Rohrer MD. 1989. Determination of the transition air temperature from snow to rain and intensity of precipitation. WMO TD No.328, International Workshop on Precipitation Measurement (ed. by B. Sevruk), St. Moritz, Switzerland, (Instruments and Observing Methods Report No. 48), 475–482.
Steinacker R 1983. Diagnose und Prognose der Schneefallgrenze. Wetter
& Leben 35: 81–90.
Ye, H., Cohen, J., & Rawlins, M. (2013). Discrimination of Solid from Liquid Precipitation over, Northern Eurasia Using Surface Atmospheric Conditions, Journal of Hydrometeorology, 14, 1345–1356. http://doi.org/10.1175/JHM-D