The initiation of a Snowball Earth event would involve some initial cooling mechanism, followed by runaway cooling due to increasing ice accumulation. The initial cooling could be facilitated by an equatorial continental distribution, which would increase the Earth's albedo near the equator, where most solar radiation is incident.
This arrangement would also allow rapid, unchecked weathering of continental rocks, a process that absorbs the greenhouse gas carbon dioxide from the atmosphere, resulting in further cooling.
Alternatively, changes in solar energy output or perturbations of Earth's orbit could act as a trigger. However the initial cooling comes about, resultant ice accumulation would reflect solar energy back to space, further cooling the atmosphere and generating more ice cover.
This feedback loop could eventually produce a frozen equator as cold as modern-day Antarctica.