Perhaps you’re looking in the wrong place for the answer. The ignition system is only part of the driveline that makes the whole thing work. A problem like this one could easily be caused by a problem in the fuel system.

In fact, the fact that the problem only happens in cold weather would make a lot of mechanics check the fuel system before fiddling with the ignition. That’s because, when an engine is cold, the fuel and air mixture needs more fuel and less air to get the thing started initially. If there’s a problem in the fuel system such as a clogged or dirty filter, an air leak or a slack fuel pump, you could potentially see the exact symptoms you have.

The problem could also lie in the injectors or any of the electronics that are supposed to tell the engine’s computer that it’s cold outside and a richer fuel:air mixture is required.

Have the car checked out by a mechanic who will be able to check all these parts for correct operation and then start replacing bits and pieces; not the other way around.

The main things to be aware of are the start-up knock in the engine that plagued the Gen III, also the rear suspension clunk due to warn bushes, and the rear tyre wear.
 

THE VX Calais weighs 1620kg, 220kg more than your VN Calais. This will certainly have an adverse effect on fuel consumption. Also, the ECOTEC V6 engine produces 152kW, whereas your VN put out 127kW. So the extra power is coming at the expense of fuel consumption. Perhaps other readers can let us know what they're getting from their VX models to compare with yours, but I reckon what you're getting is about on the mark.