Park closes at 1am (and NYPD is diligent about getting everyone out), so "Midnight Ride" should be more like "evening ride".
As one who does 99% of their weekly mileage (on bike and foot for the past 4 years) in Central Park at night, after 9pm always, (and who cannot possibly conceive of riding in the early morning) I will say it's warmer at night in the winter (though still plan on freezing).