Saudi Arabia has recently begun promoting renewable energy as a potential alternative to fossil fuels for domestic power generation. In order to efficiently connect wind energy to the existing power grids, reliable wind forecasts and an accurate way of quantifying the uncertainties of these forecasts are required. Motivated by a data set of hourly wind speeds from 28 stations in Saudi Arabia, we build spatiotemporal models for short-term probabilistic forecasts of wind vectors. Traditionally, wind speed and wind direction have been considered independently, without taking dependencies into account. However, in many situations, for example, energy management, it is essential to have information on the bivariate nature of the wind. We compare a coregionalization model for the wind vector with a univariate spatiotemporal model for the transformed wind speed in terms of sharpness and calibration. In both cases the linear predictor is a function of covariates, a smooth function to capture the daily seasonality in the wind and a latent Gaussian field to model the spatial and temporal dependencies. Substantial improvements in reliability are observed when modelling the full bivariate structure instead of only considering speed. Furthermore, the bivariate model has the advantage of also producing forecasts for the wind direction. A Bayesian framework is used to obtain forecasts that are accurate and reliable, even at stations without observations, with relatively low computational cost. Simulated high-resolution data from a computer model are used to validate spatiotemporal forecasts. A detailed analysis on this case study shows how increasing the number of locations can improve the forecast performance.