The geologic evidence for Snowball Earth (multiple ones, actually) is extremely strong. It is almost impossible to explain the re-emergence of banded iron formations without it.

The hard part is explain is how photosynthetic life survived. The Slushball Earth hypothesis holds that there was a band of thin ice near the equator. This has some severe problems though. For one, it isn't climatologically stable. The oceans in SE were covered by "sea glaciers," which were floating glaciers thicker near the poles, which flowed to the equator. These flowed due to the weak hydrologic cycle, with ice experience net sublimation near the equator. These would have overridden any areas of thin or nonexistent ice.

A hypothesis that is getting more traction is that narrow equatorial rift seas (like the Red Sea) would have prevented inflow of the sea glaciers enough for thin-ice refuges to exist. These kind of seas probably existed, because this was occurring as the supercontinent Rodinia was beginning to break up.