This paper proposes a new methodology to simulate wind fields that are non-orthogonal to the structure and to the traffic direction, and it presents the first wind-vehicle-bridge interaction (W-VBI) analysis framework to account for skew wind effects on the driving safety. The three-directional skew wind fields that are generated match well the target frequency content and correlation properties along the deck. The W-VBI methodology is applied to the study of vehicles crossing a long bridge for a wide range of wind incidence angles. It is observed that even though purely cross-winds increase the vehicle-bridge interaction, skew headwinds are more likely to cause driving accidents.