Answer:
The average annual snowfall is anywhere from about 23" to 28", but it usually melts within a week after a major snowfall. You have to go to Central Park to see accumulation on the ground. For example, when you're in Central Park, there can be 6 inches, but when you go to Manhattan there's just a trace of slush on buildings and on the sidewalk. Most of the mix is rock salt used for snow removal.
The snow might come in a 1 to 2-day snowstorm, and will remain on the ground for 4-6 days typically. Then suddenly a sunny 50°F day will make the snow melt in a few hours due especially to the urban heat island. Then 3 days later, you'll see some flurries, and they will melt 2 days later. Then another "big" snowstorm.
The monthly breakdown of average snowfall in New York City (Central Park) is as follows:
November: 0.9"
December: 5.5"
January: 7.5"
February: 8.5"
March: 5.1"
April: 0.9"
Frequency of Major Snowfall
The rest of New York State gets plenty of snow, but New York City doesn't. To some residents, it seems like it never snows in New York City. And when it does, it melts overnight anyway. The recent blizzard (February, 2010) was the first major one since December 2004 or January 2005. According to news reports, New York City public schools had only had 3 "snow days" in the last 6 years.