The blaze broke out at the Fairfield Suburbia Gardens on Great East Neck Road just before 7:30 p.m.
The first fire hydrant that responders hoped to use was covered in snow, so they used an alternative, delaying water supply to fight the fire.
One firefighter and two residents suffered minor injuries and were taken to a nearby hospital.
Two second-story apartments were extensively damaged, and 10 more apartments had water and smoke damage.
It was not clear when any of the 50 displaced residents would be allowed to return to the building.
The Red Cross assisted 19 adults and two children across 12 apartment units. Others from the complex went to stay with family and friends.
Residents were temporarily brought over to Our Lady of Grace Roman Catholic Church by the local fire department to stay out of the cold.
The cause of the fire is under investigation.
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