May have been three times even: in addition to the two Neoproterozoic "snowball earth" episodes they discuss here, there's also pretty decent evidence for an even older (~2.2 Ga) Paleoproterozoic one [1]
The Earth has been covered by ice multiple times in prehistory, but it has never been covered by land (in fact, it's unlikely that even a majority of Earth's surface was above sea level).
Hold on one minute! Geologist here -- you're partially right, but "sea glaciers" are absolutely part of the theory! Just to give you a snippet of the sort of things we're considering, here's one relevant quote from the abstract of a 2017 paper on the subject [1]:
> Some previous models have suggested that tropical open ocean or thin‐ice cover is possible; however, its viability in the presence of kilometer‐thick sea glaciers flowing from higher latitudes has not been demonstrated conclusively. Here we describe a new method of asynchronously coupling a zonal sea‐glacier model with a 3‐D global climate model and apply it to Snowball Earth.
As it happens, the key defining characteristic of a glacier is its ability to flow, i.e., "a persistent body of dense ice that is constantly moving under its own weight" [2]. While today this mostly only only happens on top of the continents, models suggest that the Neoproterozoic snowballs may have had both normal (thin, brittle, non-flowing) sea ice and flowing sea glaciers! The contrast actually ends up being important in that [3]:
> Even if thin ice was not present in the tropical ocean, it could still have prevailed on large, low‐latitude lakes and confined seas like the modern Mediterranean, protected from planetary‐scale sea‐glacier flow by surrounding continents. This, by itself, may have provided sufficient refugia to explain the survival of photosynthetic algae and other marine organisms.
There's a surprisingly large number of papers on this, actually [4].
I've worked a little bit on things relevant to this, previously discussed at https://news.ycombinator.com/item?id=18798130
[1] https://www.pnas.org/content/102/32/11131.short