The upper $100m$ to $150m$ of the polar ice sheet, called the firn, has a time-dependent density due to seasonal variations in the surface temperature, snow accumulation and surface melt events. We present RF simulations of an in-ice neutrino-induced radio source that show that these density anomalies create variations in the amplitude and propagation times of radio signals propagating through the polar firn at Summit, Greenland. The received power from signals generated in the ice that refract within the upper $\sim 15m$ firn are subject to a seasonal variation on the order of 10%. These variations result in an inherent and geometry dependent background uncertainty on the reconstructed neutrino energy and arrival direction for detectors using ice as a detection medium.