It could be a lot of things - so here are some more ideas to keep you going.
White smoke on start is probably (but not always) vaporised diesel fuel caused by one or more cylinders not having enough heat to burn the fuel on start up, by the time it comes round again it's going faster (so less heat loss and more oomph) and it works just fine (I would check glow plugs - not that normal in a good running 300tdi but it is cold at the moment).
The white smoke could also be water getting into one or more of the cylinders, when you were towing was the temp getting up awfully high? Check for coolant loss, and check your oil for white emulsion.
Also when you were towing, the engine was running fine then it did it, so it would not make sense for the engine to suddenly mis on a cylinder or two leading to diesel vapour UNLESS there is a compression problem - when you were in 4th going up the hill, was the vehicle going quite slowly, i.e. low engine revs?
Last of all, was it defiantly white, not a light grey? It could be oil, YES I know oil burns blue... MOST of the time; if oil gets into the cylinders it can also burn or more accurately vaporise into a grayish smoke. This is because it is not entering the cylinders in a calculated spray pattern, but rather leaking or blowing in.