Snow over sea ice affects the overall radiative balance of the polar region by modulating the planetary albedo and influencing sea ice growth. In satellite altimetry, snow is a major source of uncertainty in sea ice thickness estimates, especially with Ku-band radar altimeters. This is because conventional algorithms assume the primary scattering occurs at the snow/ice interface which may not hold for all snowpacks. In particular, complex snow morphological features, including wet snow and/or ice lenses, can shift the main scattering horizon toward the snow surface. These snow features may be particularly prominent over Antarctic sea ice. This study investigates how the properties of the snowpack in the Weddell Sea influence Ku-and Ka-band altimeter waveforms, particularly in the context of extreme conditions and complex snow stratigraphy. Using an adapted waveform model, we deconvolute radar echoes into contributions from the snow surface, snow volume, and ice surface, employing both least-squares fitting and Convolutional Neural Networks (CNN). Our findings challenge previous default assumptions, revealing that snow-volume scattering is as significant as that from the ice surface. To better characterize the snow scattering effects, we propose an adapted threshold first-maximum retracker algorithm (TFMRA) for CryoSat-2 radar freeboard retrieval, identifying a 70% threshold for ice floe retracking as the most accurate based on Operation IceBridge data. The algorithm, applied in CRYO2ICE campaigns and validated against snow buoy measurements, highlights the critical role of snow in altimeter retrievals. The result is particularly important given the recent unprecedented Antarctic sea ice loss and its application for future satellite missions like ESA's CRISTAL.