The transient electromagnetic method (TEM) can capture an induced polarization (IP) signature of subsurface ice. Using numerical modeling of a horizontally layered earth, we investigate how IP in TEM can be exploited for subsurface ice detection on Earth, Mars, and the Moon. In the model we implement electrical parameters from laboratory measurements of ice, planetary regolith simulants, and terrestrial soil from the literature. In contrast to currently applied forward models, we include two Cole-Cole relaxation terms to model the dielectric relaxation of adsorbed water or salt hydrate in addition to the relaxation of ice. On Earth, IP signals of shallow layers of silt mixed with 44-100 vol% ice embedded in resistive host layers of 3 k Omega m can be detected. Both at mid (45 degrees N) and lower (35 degrees N) latitudes on Mars, meter thick layers of massive ice can be detected at 10 m depth if the ice contains salts. Corresponding layers of 60 vol% ice mixed with Martian regolith simulant show similar detectability. For IP signals of lunar ice to be detected in ice volume fractions of 7.4%-46%, a development in TEM technology is required, including mitigation of early time interference, or enhancing the signal to noise level.