Cloud detection is an important pre-processing step that allows us to significantly reduce the amount of satellite imagery which should undergo further processing. In this paper, we investigate the impact of training set selection on the abilities of fully-convolutional neural networks for this task. Our experiments, performed over a range of Landsat-8 satellite images, show that the performance of deep models can substantially vary for different training samples, especially in the case of challenging scenes, such as those capturing snowy areas.