Does landing in extreme weather conditions require any different or special training?
In some regards there is but this depends on what you consider extreme weather. 

On one hand there are physical limits to which a plane can be landed when it comes to wind both head on and cross winds. Granted they are cases they may never or only rarely come up you may simply not be able to land the plane. 

Assuming you have made it to the airport and are able to land...

There are some check lists and different procedures that me be executed for different weather. Snow and wet runways in general may see a longer landing distance and roll out however this is not "special" training as landing distance should always be calculated based on conditions. 

Approaches are flown as published but changing winds and weather may cause the pilot to react differently or do different things to fly the approach. For example if you compare a calm wind approach to a dry runway with a wind sheared approach to a wet runway you may see some differences. The pilot may elect to come in a few knots over Vref and possibly with less flaps in a wind shear situation. Again this is not special training as much as it is standard. 

On a contaminated runway the pilot may chose to preform something like a short field landing so as not to potentially collapse the nose gear. All pilots (even GA) are trained in this maneuver. There are so many possible situations here it would be hard to train for ever one but some are trained for or a checklist exits.

Side Story: I was talking to a commercial pilot recently who flies the 777 and he was telling me a story of a time during training in the sim where they gave them heavy rain and 40Kts of wind shear (no one could successfully land the plane that day in his group in the sim). So they do at least throw situations like that at pilots in the sim, if they do it all the time I cant say.