Did the surfaces of the oceans freeze over entirely during the snowball Earth periods?
By looking at the recent literature on the question, I see neither a consensus or a definitive answer on the extent of the snowball earth.

Since the Neoproterozoic Snowball Earth event is more recent, there seem to be more evidences available and therefore more relevant research on this event than the 2.1 BY one - and will consider in the following only the latest event.

This paper suggest that the ice cover was likely global but some open water would have persisted in equatorial regions where complex life would have been able to survive during the glaciation.

This other paper suggest that glaciogenic sequences (sedimentary rocks containing  sediments deposited by glacier actions, for modern analog non-consolidated examples see till or moraine) in high latitudes (North) contains fragments of carbonates which was likely formed near the equatorial zone and somewhat transported by glacier action.

This yet another paper modeled how glaciation likely reach the equator, where this paper suggest that open sea must exists.

Other papers suggested that once a significant part of the Earth was covered by glaciers, albedo effect significantly cooled the planet until some kind of massive volcanic eruption interrupted the cycle.

The only consensus I figure is that it most likely happened (a late Proterozoic Snowball Earth Event) but it still remain to be seen if a thick cover of ice 'a la Encalade' covered the Earth at one time or another, or not.