The current criteria that need to be met for a storm to be classified a blizzard are:
for at least 3 consecutive hours sustained winds of 35 mph (30 knots) or greater, heavy snow (at least 1 inch per hour) and visibility of under 1/4 mile due to heavy or blowing snow. Blizzard "conditions" only require the 35 mph winds and visibility of under 1/4 mile due to heavy or blowing snow.
Note, in 1982 criteria for a storm to be classified a blizzard were revised to the current criteria. Prior to 1982, the criteria also included a relative humidity level of 100% and a temperature of 20 degrees F (-7 Degrees C) or lower.
Thus, prior to 1982, the only official blizzard to hit New York City was the Blizzard of 1888.