How does operating in an air mass that is significantly colder than standard temperature affect an aircraft's altimeter reading?

1. The altimeter will indicate an altitude higher than the aircraft's actual (true) altitude.
2. The altimeter will indicate an altitude lower than the aircraft's actual (true) altitude.
3. The altimeter reading will be unaffected, as pressure is independent of temperature.
4. The altimeter will fail to register changes in altitude and will freeze at the departure elevation.