How will the altimeter read in air colder than ISA? When flying in air which is colder than ISA (International Standard Altitude), how will the altimeter read compared to true altitude?

My manual says the altimeter will over read - why?
Air expands as the temperature increases and it compresses when the temperature decreases. 



image source: aviationweather.ws

When it is colder than ISA, the air column is compressed and therefore you are flying lower than the altimeter is indicating. In other words: the altimeter will over read in cold air. 

So to fly safely over an obstacle at a cold day, you have to add extra margin to the obstacle's height, because your altimeter will show a higher altitude than your true altitude.