Thermal contraction cracking of permafrost produced sand-wedge polygons at sea level on the paleo-equator during late Neoproterozoic glacial episodes. These sand wedges have been used as evidence for high (≥54°) paleo-obliquity of the Earth’s ecliptic, because cracks that form wedges are hypothesized to require deep seasonal cooling so the depth of the stressed layer in the ground reaches ≥1 m, similar to the measured depths of cracks that form wedges. To test the counter hypothesis that equatorial cracks opened under a climate characterized by a strong diurnal cycle and low mean annual temperature (snowball Earth conditions), we examine crack formation in frozen ground subject to periodic temperature variations. We derive analytical expressions relating the Newtonian viscosity to the potential crack depth, concluding that cracks will form only in frozen soils with viscosities greater than ∼1014 Pa s. We also show numerical calculations of crack growth in frozen soils with stress- and temperature-dependent rheologies and find that fractures may propagate to depths 3–25 times the depth of the thermally stressed layer in equatorial permafrost during a snowball Earth because the mean annual temperature is low enough to keep the ground cold and brittle to relatively great depths.