Surface wind is one of the most important atmospheric fields in climate research. Accurate prediction of high spatial resolution surface wind has a wide variety of applications, such as renewable wind energy and forecasts of extreme weather events. General circulation models (GCMs) study climate system on a global scale. Their main issues are the low resolution of the modeling results and high computational costs. One of the solutions to these problems is statistical downscaling. Statistical downscaling methods discover functional relationships avoiding computationally expensive high-resolution hydrodynamic simulations. Deep learning methods, including artificial neural networks (ANNs), are one of the typical machine-learning approaches approximating complex nonlinear relationships. In our study, we explored the capabilities of statistical 5x spatial downscaling of surface wind over the ocean in the North Atlantic region. Low-resolution input data and high-resolution validation data were provided by RAS-NAAD 40-year hindcast. We applied several downscaling methods, including bicubic interpolation as a reference solution, various discriminative convolutional neural networks (CNNs) such as Linear CNN, Residual CNN, CNN with skip connections, and generative adversarial network (GAN) based on SR-GAN. We also compared downscaling results in terms of RMSE, PSNR and other quality metrics including the ones representing the reconstruction of extreme winds. We evaluated the computational costs and the quality of different methods and reference solution to identify advantages and lacks of machine-learning downscaling. As a result, both discriminative and generative ANN-based downscaling methods have not outperformed reference solution in downscaling quality. Nevertheless, for further research, we consider GANs as the most promising ANN architectures for surface wind downscaling based on their fine-structure modeling ability.