Covering the frontal air intake on any kind of car in winter is a technique from the bad old days and supposedly achieves a faster warm-up in winter so you have demisting/defrosting quicker. You could buy internal radiator blinds, like a roller blind, with dashboard control, or a smart looking flexible external covers with flaps and press studs. (These protected the front end paintwork too, and were highly regarded by owners of things like Rover P4 and other 1950s vehicles.) Cars often did not have thermostats, and sometimes not a water pump, in those days so there was no other means of control. I have seen Minis with aluminium foil on most of the grille but never needed to do it myself, even in several very cold winters.
If you can get a Mini to run at -40 deg C, you may lose so much heat from the block, head, transmission case etc that you need to reduce airflow to get it up to running temperature. The oil temperature really MUST get up to a sensible value, or lots of things will work badly, and wear. Changing gears will be a misery, etc... If the water temperature remains low it is not quite so destructive. But various experts here will tell you more than I know about the evils of running too cold. My Minis usually had the opposite problem!