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Preliminary data from the National Weather Service, collected in Central Park, put this month's average temperature at 24.1 degrees Fahrenheit. That puts this year as the third coldest February since we started recording temperatures in Central Park in 1869. We haven't had a February this cold since 1934, when the average came in at a frigid 19.9 degrees.
Here's a chart from the National Weather Service with data from the coldest Februaries on record:

National Weather Service
In the last 80 years, New York City has also seen one January that was colder than this year's February. That was January 1977, which averaged 22.1 degrees.
This chart shows the top 10 coldest months ever in New York City. February 1934 still takes the cake.

National Weather Service
New Yorkers have also endured 11.9 inches of snow so far this month - a pretty normal amount for February.
Still, after making it through 21 days in the past month with below-freezing averages, March - and its (hopefully) balmier temperatures - is starting to look pretty welcoming.