im no mechanic but in cold eropean and even alpine regions in australin winters, they do restrict airflow to the radiator by blocking off the airflow- cardboard is just a rudimentary way of doing it.
ive had extractors on every datsun i have ever owend, never had this issue related to extractors, just issues with radiators.
personally try the cartdboard, if it works your onto something. if it doesnt,move on through process of elimination.
Actually, old chap, you are right in some respects for reasons you probably haven't thought of yet.
In really cold weather, particularly sub zero, the coolant circulation through the radiator is VERY low & since the coolant that is flowing into the engine is also VERY cold, it has the ability to soak up a LOT of heat before it becomes hot enough to open the thermostat, or to keep it open.
The amount that it opens in an efficient engine can be quite small & the flow is likewise very small.
This means that the coolant in the radiator is exposed to the icy airflow for often a surprisingly long time so if we restrict the airflow through, lets say, half of the core, then we have much less of the core now exchanging heat from the coolant into the air. [The radiator is nothing but a water to air heat exchanger remember]
Since the radiator is now a less efficient heat exchanger the coolant that reaches the block is a little warmer & absorbes less heat, resulting in an increased coolant flow which puts more hot water into the radiator core which in turn heats the [now restricted] air flowing into the engine bay & this air is being drawn into the carb.
The cylinder head/thermostat will not really see any effective change but the overall temp in the engine bay will be warmer & the engine will thank you for it.
This assumes of course that the engine does not already use a heated air induction system.
Oh yeah, the covering of a portion of the radiator will also reduce the risk of the coolant in the radiator freezing solid in extreme cold, particularly if the coolant is untreated water.
Back in the 1980's & early 90's I was the district Fleet manager for Telecom [as it was known back then] based in Goulburn. My teritory covered a fair bit of south west NSW including Cooma, Berridale, Bombala & the snowfields.
In winter I noted with interest the number of private cars at the various repairers that we used that suffered from this exact condition.
Stock engines with extractors that ran fine in the summer but were absolute dogs in the bitter depths of winter. My own Valiant fleet car was also a victim of this when I had the cracked manifold replaced with extractors in the summer of 1980. [I was the manager, I could get away with this sort of thing]
Refiting a stock manifold rectified the situation overnight & this is how several of the local yokels cars were fixed also. Additionally, I blocked off a portion of the radiator in that Valiant & in my 1200 Ute when in sub zero temperatures & reaped the benefit.