If the grid frequency is not stable enough (i.e. demand outstrips supply) any type of power plant will trip off line when the protection circuitry kicks in. Anything else risks damage to transformers and industrial machinery downstream.
The nuclear plant's turbines were literally on the "roof" of the reactor complex completely in the open. Nuclear regulations only require the reactor itself to be enclosed and protected.
No shit the turbines froze over. They ignored reports advising them to fully enclose the plant for years.
The turbines have superheated steam flowing into them directly from a source of practically unlimited heat. The only way for them to freeze over would be for the plant to have already shut down.
Loss of cooling water to the condencer is bad news for any thermal power plant. It can lead to damage to the LP turbine through poor steam quality.
I was perhaps a bit too hasty in my initial statement, clearly this reactor tripped because of the cold. I'm not an expert but given a nuclear power plant produces literally gigawatts of low grade waste heat it feels like that should have been possible to work around i.e. for example by bleeding cooling water back at the intake.