A neural network model recently developed for fog nowcasting from surface observations is summarized in its features, paying attention to its particular learning structure (weighted least squares training), introduced because of the nonconstant errors associated with the estimation of visibility values. We apply it to a winter forecast of meteorological visibility in Milan (Italy). The performance of this model is presented and shown to be always better than persistence and climatology. Finally, we introduce a bivariate analysis and a network pruning scheme and discuss the possibility of identifying the more significant physical input variables for a correct very short-range forecast of visibility.