Nik_2213 said:

What is known of Thermohaline circulation during 'Snowball Earth' episodes ?

As ice forms on the surface of the oceans, salt is not bound by the ice, so salt content and the density of the seawater increases where ice forms. That dense water sinks and flows as a saline current from areas of greatest ice formation. At the same time, the surface ice forms a blanket that reduces the geothermal heat flux, warming the saltwater, and causing it to rise. It is hypothesised that those two processes combine to mix the seawater, rather than to stagnate and stratify the oceans.

Nik_2213 said:

Sufficient to maintain a semblance of prior circulation, though ?

Thermohaline currents can be generated by surface evaporation, or by ice formation, both latitude dependent. The ocean floor is deeply scoured by thermohaline currents. Those undersea landforms can now be interpreted as being due to different generation mechanisms near the surface, at different times.