The influence of internal inhomogeneities within hydrosol particles on the polarization characteristics of light is investigated by combining an accurate coated sphere (core-shell) single-scattering model with a radiative transfer model that employs Stokes formalism and considers refraction of direct solar radiation at the air-water interface followed by single scattering. A Junge particle size distribution is assumed. Variations in what we call the "linear polarization phase function" (the degree of linear polarization as a function of scattering angle and the E-vector orientation as a function of scattering angle) are examined as a function of variations in the characteristics of the hydrosol particles. An extensive sensitivity study on the influence of variations in the real and imaginary parts of the refractive index of both the core and shell of the hydrosol particles and on the influences of variations in the ratio between the core radius and shell radius is conducted, varying the values of these parameters over the entire parameter space documented in the literature for actual hydrosol particles. In addition, calculations are conducted for specific parameter combinations in order to demonstrate the influence of some of the most important groups of hydrosols, namely, phytoplankton, gas bubbles, carbonaceous hydrosols, and mineral hydrosols, on the polarization field under water. Variations as a function of solar zenith angle are also investigated. Due to the assumption of single scattering, the results presented are relevant to conditions of low wind speed and a low scattering optical depth and/or low single-scattering albedo within the water body (clear to semi-turbid waters at shallow geometric depths and/or moderate to strong absorption within the water body) outside of Snell's window. Possible implications for aquatic animal polarization vision, for light polarization pollution, and for remote sensing are discussed.