Amtrak has annulled all Saturday trains on the Shoreline between New York and Boston because of weather. In Connecticut as far north as Stonington total snowfall is reported as 4 inches so why can't trains run as far as New London?
Providence reports 12 inches of snow. That is a lot deeper but I have taken the train from New York to Providence in past years when the snow was deeper than that. No doubt there would be delays. But why just shut down the service.
Massachusetts reports up to 20 inches of snow. Again, that would cause delays but why shut down the service? Amtrak runs through much deeper snow in the mid-west.
A real advantage of trains is that they run when nothing else can get through, when major highways are shout down and planes cannot fly. At least that used to be true.