Predicted forty years ago, supersolids have received renewed interest recently after a possible observation in 4He. While the existence of supersolids is still controversial on the experimental side, numerous examples of such phases have been identified theoretically. To investigate a new route to such exotic quantum phases, we have made a theoretical study of the strong quantum fluctuation e" ects in a special kind of polarized antiferromagnet that has spin-ice properties at the classical limit. (Full text)