I do not know which service fjor is quoting from so I can't claim consistency. It seems the highs will be in the high 30's/low 40's the lows/overnight high 20's/low 30's. There is some chance of rain, but nothing on any service is claiming anything near what you fear. From my point of view, seems what they are predicting falls on the mild and very dealable side of things for February in NYC.

I checked weather.com, weather underground, and accuweather (accuweather having the lowest temperatures of them all).

See ya Friday!