Why does your car jerk when its cold?

Perhaps it is because of the cooling/heating system that's having trouble specially when your car is dealing with extreme temperatures. The coolant overflow tank is one parts of the system that usually regulates this but of course, there'll be times that it will inevitably fail.

It is a result of the air to fuel mix , when the intake is cold the fuel doesn't vaporize as well causing uneven fuel delivery to the cylinders. Once the intake and system warm up it should normalise, but most newer vehicles have a pre-heat device to keep this from happening, if this is a newer vehicle , you might want to have it checked.