This study presents an analysis of seasonal variations in the atmospheric muon neutrino flux, using 11.3 years of data from the IceCube Neutrino Observatory. By leveraging a novel spectral unfolding method, we explore the energy range from 125 GeV to 10 TeV for zenith angles from ${90}^{\circ }$ to ${110}^{\circ }$, corresponding to the Antarctic atmosphere. Our findings reveal that the differential measurement of the amplitudes of the seasonal variation is consistent with an energy-dependent decrease reaching ($-\,4.5$ ± 1.2)% during Austral winter and increase to (+ 3.9 ± 1.3)% during Austral summer relative to the annual average at 10 TeV. While the unfolded flux exceeds the model predictions by up to 30%, the differential measurement of the seasonal to annual average flux remains unaffected. The measured seasonal variations of the muon neutrino spectrum are consistent with theoretical predictions using the MCEq code and the NRLMSISE-00 atmospheric model.