Electric-field $(E)$ drive of magnetic resonance in a solid has been a big challenge in condensed-matter physics and emerging spintronics. We demonstrate the appearance of distinct magnetic excitations driven by the light $E$ component in a hexaferrite ${\text{Ba}}_{2}{\text{Mg}}_{2}{\text{Fe}}_{12}{\text{O}}_{22}$. In the conical-spin state even with no spontaneous electric polarization $({P}_{\text{s}})$, a sharp and intense resonance is observed around 2.8 meV for the light $E$ vector parallel to the magnetic propagation vector in accord with the inelastic neutron scattering spectrum at the magnetic zone center. As the generic characteristic of the conical state, a weak magnetic field $(\ensuremath{\sim}2\text{ }\text{kOe})$ can modify the spin structure, leading to a remarkable change (terahertz magnetochromism) in spectral shape and intensity (by $\ensuremath{\sim}200%$) of the electric-dipole-active magnetic resonance. The present observation implies that potentially many magnets with noncollinearly ordered spins may host such an electric-dipole-active resonance, irrespective of the presence or absence of ${P}_{\text{s}}$.