Radiation transmitted through sea ice and snow has an important impact on the energy partitioning at the atmosphere-ice-ocean interface. Snow depth and ice thickness are crucial in determining its temporal and spatial variations. Under-ice surveys using autonomous robotic vehicles to measure transmitted radiation often lack coincident snow depth and ice thickness measurements so that direct relationships cannot be investigated. Snow and ice imprint distinct features on the spectral shape of transmitted radiation. Here, we use those features to retrieve snow depth. Transmitted radiance was measured underneath landfast level first-year ice using a remotely operated vehicle in the Lincoln Sea in spring 2018. Colocated measurements of snow depth and ice thickness were acquired. Constant ice thickness, clear water conditions, and low in-ice biomass allowed us to separate the spectral features of snow. We successfully retrieved snow depth using two inverse methods based on under-ice optical spectra with 1) normalized difference indices and 2) an idealized two-layer radiative transfer model including spectral snow and sea ice extinction coefficients. The retrieved extinction coefficients were in agreement with previous studies. We then applied the methods to continuous time series of transmittance and snow depth from the landfast first-year ice and from drifting, melt-pond covered multiyear ice in the Central Arctic in autumn 2018. Both methods allow snow depth retrieval accuracies of approximately 5 cm. Our results show that atmospheric variations and absolute light levels have an influence on the snow depth retrieval.