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First, establish firmly in your mind that an altimeter is simply a pressure guage. It does not measure air density.
To visualize what happens, start by imagining what would happen to the atmosphere if you froze the entire planet. The atmosphere would become more dense as all the gas contracted. As it contracts the "top" of the atmosphere gets lower. The whole thing shrinks. So the pressure at a fixed true altitude (top of Mt. Everest say) gets lower. If you kept freezing the planet eventually the top of Mt. Everest would be poking into space.
Another way to visualize it is to imagine that the air pressure you are flying in is being supported by all the air below it. As you cool that air down it shrinks, and the air you are in drops. Hence your indicated altitude is lower than your true altitude.
Another way to visualize it is to imagine that the air pressure you are flying in is being supported by all the air below it. As you cool that air down it shrinks, and the air you are in drops. Hence your indicated altitude is lower than your true altitude.