Not yet reviewed by Pith; the record is open.

The study of the Cosmic Microwave Background (CMB) lensing potential has established itself by now as a robust way of probing the physics of large-scale structure growth. The most common estimators of the lensing potential are derived under the assumption of Gaussianity of the matter distribution and in the Born approximation of the photon diffusion. In this paper we study the performance of quadratic estimators when applied to realistic sky maps extracted from multiple-lens ray tracing techniques in cosmological $N$-body simulations. These are expected to model accurately the effects due to the non-Gaussianity of the matter distribution induced by its nonlinearity and the deviation from the Born approximation. We show that both these effects on their own lead to reconstruction biases, but these tend to partially cancel each other when both these effects are considered together. We forecast the impact of these biases on the estimation of cosmological parameters for future high-sensitivity CMB experiments like CMB-S4. We find that the cold dark matter density, $\Omega_\textrm{cdm}$, the optical depth to reionization $\tau$, the amplitude of primordial inflationary perturbations, $A_s$ and the sum of neutrino masses, $M_\nu$, could be biased at the 1-2$\sigma$ level, if no external data set is used. We also observe a reduction of the bias if external data like baryon acoustic oscillations (BAO) is included.