Measurements of gravitational lensing of the cosmic microwave background (CMB) hold the promise of yielding unique insights into cosmology at high redshift. Uncertainties due to baryonic effects associated with galaxy formation and evolution, including gas cooling, star formation, and feedback from active galactic nuclei (AGN) and supernovae, have typically been neglected when forecasting the sensitivity of future CMB surveys. In this paper, we determine the impact of these effects using four suites of hydrodynamical simulations which incorporate various prescriptions for baryonic processes, namely OWLS, BAHAMAS, Horizon, and IllustrisTNG. Our analysis shows characteristic power suppressions of several percent in CMB lensing due to baryonic effects, compared to dark-matter only simulations, at experimentally observable angular scales. We investigate the associated bias in the inferred neutrino mass for experiments like the upcoming Simons Observatory and CMB-S4. Depending on the experimental precision and the strength of the baryonic feedback within the simulations, biases in the neutrino mass sum show significant dispersion, ranging from very small to an over-estimation by 1.1$\sigma$. We conclude that baryonic effects will likely be non-negligible for a detection of neutrino mass using CMB lensing.