What would the altimeter indication be through a cold front? Cold air is heavier than hot air because of its greater density, so the QNH of an airport inside a cold front would be higher. Flying towards the cold front would be, "low to high, hello sky".

But I also know that for altimetry, cold air generates lower pressure inside the pitot-static system than warm air, and it would increase the altimeter reading, so "hot to cold, look out below".

I'm confused because of the 2 contradictory factors. If we fly towards a cold front without adjusting the altimeter setting, would there be an increase or a decrease in the indicated altitude?



There's an ATP question:


  Event after an aircraft passes through a front into the colder air.


Answer:


  Atmospheric pressure increases.


Well, yes, that's why QNH would be higher, but our altimeter would sense the temperature and "feel" a decrease in atmospheric pressure.

So, what would be the real indication of the altimeter in this situation?
There are two altimeter reading questions here, what happens when:


flying towards the cold front (third paragraph)
flying into the cold front (headline)


According to this University of Illinois web article following things happen:

Flying towards a cold front (or in the article the front is approaching you, but it makes no difference):


pressure drops steadily
temperature is steady


Passing through the front:


pressure reaches minimum, then rises sharply
temperature drops suddenly.


So, to answer both questions, assuming you are flying at relatively low altitude and maintaining it in reference to your altimeter and you do not adjust QNH:


Approaching the cold front you would steadily drift downwards: from high to low, look out below!
Passing through the front you would need to climb to maintain steady altimeter reading: low to high, hello sky!


You see, the question is about what happens to altimeter reading, but since the vertical position of the aircraft is maintained in reference to the altimeter reading, whether it's you or the autopilot flying, the altimeter reading would not change. The vertical position of the aircraft would be instinctively or algorithmically adjusted to keep the reading at a selected value.

What happens at altitude, is (for now) somewhat beyond me (pressure gradients and stuff), so  I dare not answer that scenario here yet.



P.S. a private pilot should not fly through a cold front: it's not a good place for small planes to be in...