The Finite-Difference Time-Domain (FDTD) method in cylindrical coordinates is used to describe electromagnetic wave propagation in a cold magnetized plasma. This enables us to study curvature effects in toroidal plasma. We derive the discrete dispersion relation of this FDTD scheme and compare it with the exact solution. The accuracy analysis of the proposed method is presented. We also provide a stability proof for nonmagnetized uniform plasma, in which case the stability condition is the vacuum Courant condition. For magnetized cold plasma we investigate the stability condition numerically using the von Neumann method. We present some numerical examples which reproduce the dispersion relation, wave field structure and steady state condition for typical plasma modes.