That's strange.
The feedwater pumps are fed from the turbine condensers by condensate pumps. None of that part of the system would be affected by outside weather conditions.
Depending on the siting of the plant and it's construction, it's cooling the condensate with natural water sources, or it's running on a cooling tower. I can't see any kind of problem with a condenser running on natural water sources as the heat sink. Navy reactors routinely run in the North Atlantic and the sea water temps there can go down to 29 degrees. It actually boosts the Carnot efficiency of the power plant.
But if they're using a cooling tower...did they forget to put anti-freeze in the circulating water and the pipes froze? Loss of cooling water would trip the turbines off line and that would dump the feedwater system...
...stupid articles never go into the interesting details.
But...the other half of the reactor system wasn't affected...this might be completely unrelated to the moderate weather they're experiencing.
South Texas Nuclear plant uses a large cooling ponds, not towers.

Power was down for three days.
- - - - - -
“It’s very rare for weather issues to shut down a nuclear plant," said Brett Rampal, director of nuclear innovation at the Clean Air Task Force. "Some equipment in some nuclear plants in Texas has not been hardened for extreme cold weather because there was never a need for this.â€
According to the Nuclear Regulatory Commission, the shutdown of the nuclear reactor was caused by a disruption in a feedwater pump to the reactor, and that caused the plant to trip automatically and shut down early Monday.
There was no underlying danger to the reactor itself, Rampal and other experts said, and the trip was part of normal safety operations protocol.
https://www.washingtonexaminer.com/policy/energy/how-and-why-a-nuclear-reactor-shut-down-in-texas-cold-snap-when-energy-was-needed-most- - - - - - -
"At 0526 [CST] on 02/15/2021, Unit 1 automatically tripped due to low steam generator levels. The low steam generator levels were due to loss of Feedwater pumps 11 and 13 (cause unknown).
"Auxiliary Feedwater and Feedwater Isolation actuated as designed. All Control and Shutdown Rods fully inserted. No primary or secondary relief valves opened. There were no electrical problems. Normal operating temperature and pressure (NOT/NOP) is 567 degrees F and 2235 psig.
"There were no significant TS LCOs entered.
"This event was not significant to the health and safety of the public based on all safety systems performed as designed. Unit 2 was not affected. Decay heat removal is being controlled via Steam Dumps. [Auxiliary Feedwater is supplying water to the Steam Generators.] Offsite power is in the normal electrical lineup.
https://www.nrc.gov/reading-rm/doc-collections/event-status/event/2021/20210216en.html