Unfortunately Manhattan doesn't seem like a great place for bikes. The weather is just too variable. Some daredevils will be out in any weather but for most people it's just not feasible about half of the days of the year.
Not that helicopters make any more sense. The city needs some car bans, and yes, bicycles are part of replacing that. But only mass transit will be able to move enough people when there's a foot of slush on the ground.
Weather in New York is perfectly fine for biking. If you can walk outside you can bike. Both means of transportation are equally resilient to bad weather. What you need is protected bike lanes, so you can bike relaxed and holding an umbrella if necessary, as millions of people do every day in Netherlands and other European countries.
Not that helicopters make any more sense. The city needs some car bans, and yes, bicycles are part of replacing that. But only mass transit will be able to move enough people when there's a foot of slush on the ground.