This article deals with the problem of computing surface concentrations for two types of river ice from digital images acquired during freeze-up. It presents the results of attempting to solve this problem using several state-of-the-art semantic segmentation methods based on deep convolutional neural networks (CNNs). This task presents two main challenges—very limited availability of labeled training data and presence of noisy labels due to the great difficulty of visually distinguishing between the two types of ice, even for human experts. The results are used to analyze the extent to which some of the best deep learning methods currently in existence can handle these challenges. The code and data used in the experiments are made publicly available to facilitate further work in this domain.