Another problem for rail and subways is salt water getting into the traction motors during bad weather.
In 1979, Chicago had an unexpectedly ferocious snowstorm (resulting in 74 cm depth of snow on the ground) that closed down most everything, and resulted in the electoral defeat of the incumbent mayor.
Total removal of the snow took 59 days.
A specific problem was the surface lines on the CTA 'L', where the newer lines ran down the median of expressways (Dan Ryan on the south side and Kennedy on the north side).
Plowing the highways deposited salty snow on the 'L' tracks, and the existing rolling stock used self-ventilated electric motors where the fans sucked saltwater into the motor.
Despite hiring all of the rewinding capability in the city, these newer lines had to shut down.
On the older elevated lines, such as the "Loop" around downtown, and the Englewood/Jackson Park lines, the snow fell through the gaps between ties and caused less trouble.
Later CTA rolling stock employed ventilation input from the roof because of that history.
I don't remember any substantial problems with the third rail itself during that crisis, except for icing.