Those are contributing factors, and the small size could be part of the reason the magnetic field stopped at some point, if the core cools down too fast. But a strong magnetic field like Earth's will block the fastest parts of the solar wind from hitting the atmosphere. Without that, each particle of solar wind that hits a molecule of the atmosphere can send that molecule out into space, (beyond escape velocity) which adds up over thousands or millions of years to remove most of the atmosphere that was originally there.

Without enough pressure, liquid water will boil even at cold temperatures, and will be part of the atmosphere that is stripped away.