We study the polarization properties of the light field under a dynamic ocean surface using realistic linear and nonlinear ocean surface waves. The three-dimensional polarized radiative transfer of the dynamic ocean-atmosphere system is considered using a Monte Carlo vector radiative transfer simulation for arbitrary depth. The program is validated with measurement data taken in Hawaii during the Radiance in a Dynamic Ocean project. The main focus of this study is the influence of the wind-driven ocean waves on the polarization patterns and statistics at different optical depths under various conditions of light wavelength and solar incidence. Of special interest is the effect of the nonlinearity of the surface waves on the polarization statistics. To facilitate the study, phase-resolved direct simulations of the linear and nonlinear surface wavefields are performed using a high-order spectral method. The results show that the time-averaged degree of polarization within the Snell's window is dependent on the mean square slope of the ocean surface. Higher mean square slope, or wind speed, leads to a smaller degree of polarization. At the same time, the variability of the degree of polarization has a strong dependence on the surface roughness. A rougher ocean surface induces higher variability of the degree of polarization. The effect of wave nonlinearity can be neglected for the mean value of polarization, but is manifested in the variability of the degree of polarization, with a general increase in the variance with increasing wave nonlinearity. The present findings provide possible mechanisms for characterizing the dynamic ocean surface based on underwater polarized light measurements.