Snow cover? Maybe for a couple hours. The one and only storm you got (and myself) was Jan 19-20th 2002 aka the Foxborough Storm. The day after was about 40F and then got into the 50s and 60s for the next several days. I'm guessing whatever snow fell overnight that night was gone by about noon the next day. It was in CT.
The only season worse than 01-02 in the past 150 or so years of records in NYC is 72-73. Only 2.8" was measured that entire season.
If you dont get a flake more than it might be just as bad as 01-02 for you but that season felt like no winter at all. It was warm all the time, there were never any storm threats at all to speak of. I don't think this one will end as bad as that for NYC. You've also had less going into Feb than this season, 06-07, 07-08, 94-95, 92-93 and 91-92.