The Simons Observatory (SO) will observe the temperature and polarization anisotropies of the cosmic microwave background (CMB) over a wide range of frequencies (27 to 270 GHz) and angular scales by using both small (â1/40.5 m) and large (â1/46 m) aperture telescopes. The SO small aperture telescopes will target degree angular scales where the primordial B-mode polarization signal is expected to peak. The incoming polarization signal of the small aperture telescopes will be modulated by a cryogenic, continuously-rotating half-wave plate (CRHWP) to mitigate systematic effects arising from slowly varying noise and detector pair-differencing. In this paper, we present an assessment of some systematic effects arising from using a CRHWP in the SO small aperture systems. We focus on systematic effects associated with structural properties of the HWP and effects arising when operating a HWP, including the amplitude of the HWP synchronous signal (HWPSS), and I → P (intensity to polarization) leakage that arises from detector non-linearity in the presence of a large HWPSS. We demonstrate our ability to simulate the impact of the aforementioned systematic effects in the time domain. This important step will inform mitigation strategies and design decisions to ensure that SO will meet its science goals.