"All of these passengers from all three trains should be in Chicago by early afternoon," said Amtrak spokesman Marc Magliari.
Magliari said "blowing and drifting conditions" made the paths the trains were on too difficult to travel. However, there were full "hotel systems" on the trains that worked through the night, he added.
"At no point did trains lose hotel power," he said.
Meanwhile, at Los Angeles International Airport some three-dozen flights were canceled Monday because of the bitter cold weather in the Northeast and Midwest.
A spokesperson for the airport said more than 5,200 passengers were affected. And if the flight wasn't canceled Monday, there was a decent chance it was delayed. Passengers on at least 151 flights had an average delay of 90 minutes.
A mass of Arctic air known as a "polar vortex" is responsible for the harsh conditions, according to the National Weather Service.