Are there particular injuries that are more common when training in wet and windy weather?

Depends on condition: Windy, wet, hot, cold are all very different conditions and must be taken into account when training. Certainly a wet surface will make you more prone to a slip and fall and perhaps that would be a good track day or indoor cross training day. Hot-think fluids and sunsreen; cold-think layers. http://www.worldkeepsrunning.org/advicepage.aspx?adviceid=16.

Sprains: Spraining your ankle, severe to mild, it band syndrome, falls leading to contusion or bruising, etc.