Automated sea ice charting from synthetic aperture radar (SAR) has been researched for more than a decade, and we are still not close to unlocking the full potential of automated solutions in terms of resolution and accuracy. The central complications arise from ground truth data not being readily available in the polar regions. In this paper, we build a data set from 20 near-coincident x-band SAR acquisitions and as many airborne laser scanner (ALS) measurements from the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC), between October and May. This data set is then used to assess the accuracy and robustness of five machine-learning-based approaches by deriving classes from the freeboard, surface roughness (standard deviation at 0.5 m correlation length) and reflectance. It is shown that there is only a weak correlation between the radar backscatter and the sea ice topography. Accuracies between 44 % and 66 % and robustness between 71 % and 83 % give a realistic insight into the performance of modern convolutional neural network architectures across a range of ice conditions over 8 months. It also marks the first time algorithms have been trained entirely with labels from coincident measurements, allowing for a probabilistic class retrieval. The results show that segmentation models able to learn from the class distribution perform significantly better than pixel-wise classification approaches by nearly 20 % accuracy on average.