I wonder if, in the absence of gravity (and thus no issue of buoyancy), a spherical ice ball would form in a stream of slow moving cold water...
A disk is rotating its circumference scraping along obstructions such that the growth of ice is steered naturally to a perfect circle. This rotation has a fixed center and axis. A ball however would be scraped towards a cylinder if the same thing happened. To create a ball nature would need the same thing as someone making a wood ball on a belt grinder: vary the rotation axis. However if there are local stability min…
I guess the end result would depend on the shape of the surrounding cave and on what fraction of its volume the object would eventually fill. I don’t see a tumbling cylinder made of ice inside a hollow sphere filled with icy water remain cylindrical in shape, for example.
On the other hand, inside a relatively tall cylindrical space where the water is below freezing temperature, things could be different (does the production of M&Ms involve tumbling?)