The March 17, 2011 article Snow Slows Local Sailors' Efforts in Japan shows the above photo and says:
Poor weather conditions hampered San Diego based Sailors’ relief efforts in Japan on Wednesday.
The Black Knights Anti-Submarine helicopter squadron, assigned to aircraft carrier USS Ronald Reagan
“It is one of the first times for many that it is snowing at sea, hope you are enjoying the SoCal weather,” the CMC [Command Master Chief] said.
One of the helicopters assigned to Preble tested positive for radioactivity. According to Cahill, the contamination was cleaned up with soap and water.
The USS Preble contamination case is one of 17 detected among USS Reagan Carrier Strike Group (CSG) crewmembers.
On an official US military website it is stated: 7th Fleet observes moment of silence, reflects on Operation Tomodachi says:
March 17: Although snow and poor visibility hampered helicopter operations, helicopters from the USS Ronald Reagan strike group and Carrier Air Wing Five in Atsugi conducted 10 helicopter sorties, delivering about 10 tons of HA/DR supplies.
Additionally, in the NY Post article in the OP, Lindsay Cooper states as an eyewitness aboard the USS Ronald Reagan that it did snow.
Also, months before the articles in the OP, Roger Witherspoon reported in The Asia-Pacific Journal, Vol. 11, Issue 12, No. 1.
March 25, 2013, in the article Lasting Legacy of the Fukushima Rescue Mission: Cat and Mouse
with a Nuclear Ghost 福島救援活動の永続する遺産—核の幽霊といたち
Up on the captain’s bridge it became clear that
the ship was contaminated. It had snowed and
sailors had a snowball fight – till the sensors
revealed that the snow itself was contaminated,
having scrubbed skies of radioactive particulates.
So, while in the photograph in the OP the white stuff is soap suds, yes it did snow on the Ronald Reagan carrier group at the time of the Fukushima disaster and there was radioactive contamination which was attempted to be removed with soapy water.