Electrical control over the magnetic states of doped semiconductor nanostructures could enable new spin-based information processing technologies. To this end, extensive research has recently been devoted to examination of carrier-mediated magnetic ordering effects in substrate-supported quantum dots at cryogenic temperatures, with carriers introduced transiently by photon absorption. The relatively weak interactions found between dopants and charge carriers have suggested that gated magnetism in quantum dots will be limited to cryogenic temperatures. Here, we report the observation of a large, reversible, room-temperature magnetic response to charge state in free-standing colloidal ZnO nanocrystals doped with Mn(2+) ions. Injected electrons activate new ferromagnetic Mn(2+)-Mn(2+) interactions that are strong enough to overcome antiferromagnetic coupling between nearest-neighbour dopants, making the full magnetic moments of all dopants observable. Analysis shows that this large effect occurs in spite of small pairwise electron-Mn(2+) exchange energies, because of competing electron-mediated ferromagnetic interactions involving distant Mn(2+) ions in the same nanocrystal.