During an approach at night-time into Glasgow Airport, the crew of an easyJet A319 experienced a strong cross-wind and turbulent conditions, which created a WINDSHEAR alert and led them to perform a go-around.As they did this, PFD information including Flight Modes Annunciator, Flight Director bars, and characteristic speeds all disappeared from both PFDs. In addition, the rudder travel limiter function became unavailable, and the auto-thrust disconnected. The crew was facing a very challenging situation, and needed to use their training in back-to-basics flying and efficient Crew Resource Management.