The National Labor Relations Board is hearing arguments and determining the legality of the ongoing school bus workers' strike.
Bus company owners lodged a complaint with the board last week, though a decision is not expected any time soon.
If it's ruled illegal, the NLRB could order drivers and matrons back to work.
Meantime, union members say they will keep demonstrating while making allowances for the cold weather.
"We're taking breaks, sitting in the car, going to the store to get warmed up and you know, we're coming back out. Fifteen minutes you take a break, you come out, you walk for 45. We're trying to make it so everybody gets warm and nobody gets sick," said one striking school bus worker.
"We all want to go back to work but the mayor has to come to sort of agreement with us also. That's why it's going to be in court today," said another striking school bus worker.
Members of Amalgamated Transit Union Local 1181 went on strike last Wednesday over the city's effort to solicit new bus contracts.
The union says it wants the jobs of senior employees protected in any new contract but the city says it cannot legally guarantee those protections.
Some 150,000 school kids have been affected by the strike, a third of them with special needs.