Mine runs rough if the ambient temps are below 40f.
On yours there is an intake air heater grid that is easily diagnosed. The circuit is controlled by a relay that looks at coolant temperature. If the coolant is below a certain temp the electric grid for the air pre-heater runs for about 30 seconds, you can generally hear the idle speed come up a bit when that circuit for the heater shuts down as the pre-heater uses many amps to heat the intake air.
Check the amp draw at the wire for the grid when first running the engine. Big red wire by the 4 bolt flange on the intake manifold. I'm not sure how many mine draws I can check. Make sure the wire isn't melted by the connector at the pre-heater.
Regards, Fred