A time‐dependent, three‐dimensional, multi‐ion model of the global ionosphere‐polar wind system was used to study the system's response to an idealized geomagnetic storm for different seasonal and solar cycle conditions. The model covered the altitude range from 90 to 9000 km for latitudes greater than 50° magnetic in the northern hemisphere. The geomagnetic storm contained a 1‐hour growth phase, a 1‐hour main phase, and a 4‐hour decay phase. Four storm simulations were conducted, corresponding to winter and summer solstices at both solar maximum and minimum. The simulations indicated the following: (1) O+ upflows typically occur in the cusp and auroral zone at all local times, and downflows occur in the polar cap. However, during increasing magnetic activity, O+ upflows can occur in the polar cap, (2) The O+ upflows are typically the strongest where both Te and Ti are elevated, which generally occurs in the cusp at the location of the dayside convection throat, (3) The upward H+ and O+ velocities increase with Te, which results in both seasonal and day‐night asymmetries in the ion velocities, (4) During “increasing” magnetic activity, O+ is the dominant ion at all altitudes throughout the polar region, (5) For solar minimum winter, there is an H+ “blowout” throughout the polar region shortly after the storm commences (negative storm effect), and then the H+ density slowly recovers. The O+ behavior is opposite to this. There is an increase in the O+ density above 1000 km during the storm's peak (positive storm effect), and then it decreases as the storm subsides, and (6) For solar maximum summer, the O+ and H+ temporal morphologies are in phase; but the ion density variations at high altitudes are opposite to those at low altitudes. During the storm's peak, the H+ and O+ densities increase at high altitudes (positive storm effect) and decrease at low altitudes (negative storm effect).