Water viscosity

“Viscosity is a property of the fluid which opposes the relative motion between the two surfaces of the fluid that are moving at different velocities. In simple terms, viscosity means friction between the molecules of fluid. When the fluid is forced through a tube, the particles which compose the fluid generally move more quickly near the tube's axis and more slowly near its walls; therefore some stress (such as a pressure difference between the two ends of the tube) is needed to overcome the friction between particle layers to keep the fluid moving.” (Source Wikipedia)

One relevant point for us is that water viscosity changes with temperature in a non neglibile way between -10 and 40 centigrades, temperature that many soils can across easily in different seasons: this table shows how much. A model for water viscosity in a large range of temperatures is given by Kestin et al. [1978], which can be used in models.
Viscosity is actually so important that an entire website is dedicated to its experimental values of viscosity: viscopedia. Same information can also be read from this other informative website about water as a substance.
Viscosity variation is usually forgotten in hydrological modelling and the fact that water travels two times faster (at least) in summer than in winter is usually forgotten in any model of runoff production. It is probably time that we incorporate such effects in our modelling of infiltration, and for what regards me, in our numerical integrator of Richards equation.
When dealing with infiltration, in hydrologically realistic contexts, papers by Constanz and coworker are a standard reference, starting from Constantz [1981], Ronan et al, 1998, and Costantz and Murphy [1991]. Papers citing them are also interesting (here the Scopus list) and cover quite recent works too. We can identify two issues (the usual ones): first it is necessary to understand how viscosity variation affects equations of flow, secondly how these affect a heterogeneous landscape.
Grifoll et al (2005), in analysing the problem of water vapor transport, independently if you like or not their solutions, contains the right equations, and can be an help to write yours.
A related question is if temperature alters also the soil water retention curves. This problem is faced by a recent paper by Roshani and Sedano [2016] but it is still clearly an open problem.

I did not start really reading these papers. However, here it is their list below.

• Constantz, J. (1981). Temperature Dependence of Unsaturated Hydraulic Conductivity of Two Soils. Soil Sci. Soc. Am. J., 46, 466–470. 
• Constantz, J., & Murphy, F. (1991). The temperature dependence of ponded infiltration under isothermal conditions. Journal of Hydrology, 122, 119–128.. 
• Grifoll, J., Gastó, J. M., & Cohen, Y. (2005). Non-isothermal soil water transport and evaporation. Advances in Water Resources, 28(11), 1254–1266. http://doi.org/10.1016/j.advwatres.2005.04.008
• Hopmans, J. W., & Dane, J. H. 1986). Temperature Dependence of Soil Hydraulic Properties. Soil Sci. Soc. Am. J., (50), 4–9. 
• Jaynes, D. B. (2002). (1990) Temperature Variations Effect on Field-Measured Infiltration, 1–8. 
• Kestin, J., Sokolov, M., & Wakeham, W. A. (1978). Viscosity of Liquid Water in the Range -8 C to 150 C. J. Phys. Chem. Ref. Data, 7(3), 941–048. 
• Ronan, A., Prudic, D., Thodal, C., & Constantz, J. (1998). Field study and simulation of diurnal temperature effects on infiltration and variably saturated flow beneath an ephemeral stream. Water Resources Res., 34(9), 2137–2153. 
• Roshani, P., & Sedano, J. Á. I. (2016). Incorporating Temperature Effects in Soil-Water Characteristic Curves. Indian Geotechnical Journal, 46(3), 309–318. http://doi.org/10.1007/s40098-016-0201-y