Classification of Synthetic Aperture Radar (SAR) images is a complex task because of the presence of speckle, which affects images in a way similar to a strong noise. In this study, we investigate the use of Convolutional Neural Networks (CNNs) which can effectively learn a bank of spatial filters to simultaneously 1) reduce speckle noise, and 2) extract spatial-contextual features to characterize texture and scattering mechanism. Moreover, we combine CNN with Markov Random Fields (MRFs) for post-classification label smoothing to further reduce the effect of speckle on the land-cover map and to improve classification accuracy. We applied the proposed classification system to the analysis of a multitemporal series of Sentinel-1 images for mapping agricultural fields in Flevoland, The Netherlands. Experimental results confirm the effectiveness of the investigated approach, which outperforms standard methods.