Abnormally Cold Air Effects on Altitude Readings

[casablanca]

As for the why? That is too complicated for my first cup of coffee.
However it is quite noticeable in extreme conditions
At cruise altitude it is not a factor, unless terrain is very high, but yes cold temps affect the altimeter. Normally recommended to apply a correction when below zero....usually about 10% down to -10c, then the correction increases with temp drop.
So if temp -7 and doing an approach with mda of 330 agl, would add 33 feet to baro minimums.

It is also affected by high temps. Often we do the Ils approach at sea level airport at near 50 degree temps. At faf we are at 3000 agl,( actual)but when you look at altimeter it will read much lower like 2750.
In the case of cold weather you are lower than you think.....and a threat to strike terrain so hence the correction, but warm temps can also make your approaches high/ unstable when doing non precision approaches