Droplet spreading at an applied voltage underlies the function of tunable optical devices including adjustable lenses and matrix display elements. Faster response and the enhanced resolution motivate research toward miniaturization of these devices to nanoscale dimensions. The response of an aqueous nanodroplet to an applied field can differ significantly from macroscopic predictions. Understanding these differences requires characterization at the molecular level. We describe the equilibrium and nonequilibrium molecular dynamics simulations of nanosized aqueous droplets on a hydrophobic surface with the embedded concentric electrodes. Constant electrode potential is enforced by a rigorous account of the metal polarization. We demonstrate that the reduction of the equilibrium contact angle is commensurate to, and adjusts reversibly with, the voltage change. For a droplet with O(10) nm diameter, a typical response time to the imposition of the field is of O(10(2)) ps. Drop relaxation is about twice as fast when the field is switched off. The friction coefficient obtained from the rate of the drop relaxation on the nonuniform surface, decreases when the droplet approaches equilibrium from either direction, that is, by spreading or receding. The strong dependence of the friction on the surface hydrophilicity points to the dominance of the liquid-surface friction at the drop's perimeter as described in the molecular kinetic theory. This approach enables correct predictions of trends in dynamic responses associated with varied voltage or substrate material.