As Kevin says, the port is particularly exposed to southwestery winds. Although we talk about the Western and Eastern Docks, the port actually runs from southwest to northeast so southwesterlies blow directly across the berths with no shelter provided by the land.
The ferries are highly manoeuvrable and can manage to berth in all but the most atrocious conditions. PaulB's photo on the front page at the moment shows two DFDS ferries - the Dover Seaways making her entry with the Delft or Dunkerque in the background having just departed. Although Paul says "Large ships clearly cannot negotiate the narrow harbour in rough conditions," these two are actually nearly twice the size of two of the cruise ships which had to cancel, namely the Saga Pearl II which diverted to Harwich and the Black Watch which diverted to Portsmouth. Costa Luminosa is much larger and diverted to Southampton.
This is because cruise vessels are generally less manoeuvrable than the ferries but also have to negotiate the end of the Prince of Wales and then try to stay on the berths on the Admiralty Pier without their ropes parting due to the wind strength.
General info about operating limitations in the Port of Dover appended below for anybody interested:
http://www.doverport.co.uk/?page=OperatingLimitations