I heard that the coolant lines froze up in that power plant. This is something that better insulation, de-icing, whatever, can solve.
The whatever is called "heat trace." I work in a non-nuclear power plant in NYC, and our cooling water lines that run to outside equipment are electrically heat traced (under the insulation). Note that our fuel oil lines use steam heat tracing... you don't ordinarily use electric heat trace on lines filled with combustible liquids. Also note that we don't use anti-freeze in our fresh water recirc cooling water systems due to environmental regulations.
Another possibility where water freezing can lead to a unit trip are the small impulse lines going to instrumentation such as pressure transmitters, level transmitters and flow transmitters. These impulse lines are dead ended at the transmitters and are in tubing as small as 1/4" in diameter, so they are quite susceptible to freezing.