I recently bought a A6 allroad 3.0tdi. It has now done 13000 miles. I have noticed that the tyres are getting hot and you can smell burning rubber. On one occasion when it was icy, you could see smoke off the tyres. I don't drive particularly fast (honest!).
The Audi dealership cannot find any fault or sign of my problem, has any other forum members experienced this type of problem?

 

tires will get warm whenever you drive due to friction on the road surface. They should not, however, get "hot". Some usual causes for overheated tires are due to under inflation, brake problems, or a bad (sticky) wheel bearing. These things will also cause you to experience some other symptoms besides just a hot tire and only the tire on the affected wheel would get hot.

if you are seeing the symptoms when it is icy, it is possible that your tread is not sufficient enough to provide necessary traction for the conditions. your tires are spinning as they try to find grip and that excess friction is creating the condition you describe. How is the tread?