All great suggestions. I don't remember whether anyone mentioned one thing to watch out for about onesies or footie PJ's and cloth diapers, which is that baby's torso will probably be much longer because of the CDs, so you should size way way up (or, for onesies, you can buy crotch extenders to give a few more inches of room, which I suppose would be a nice investment if you are a true onesie devotee).
My only other thought for you is very NYC specific (we lived there for a number of years, just left when DD turned 2). The type of cold weather wear you need will depend largely on your lifestyle when you're out and about in the city. Honestly, I'd recommend that you just look at your current commuting tendencies and sort of magnify them. For example, do you take a lot of taxis, or do you own a car and drive it a lot, or do you walk everywhere, or do you use public transit? My "getting around the city" habits did not change dramatically once I had a baby. I didn't personally take taxis any more frequently. I supposed I walked more once she was born, and the awesome stroller eventually became my best friend (even though i didn't initially think I'd want one, and didn't buy one till DD was 3 or 4 months).
If baby will spend a lot of time transiting in a car and you choose to use a car seat for that (it is not legally required in NYC taxis), then a bundle me type cover is a fab solution, and you'll be able to use it again next winter.
If you plan to babywear, then I recommend that you not overdress a March baby in crazy buntings and things, but instead wear a large jacket that zips over baby and get him/her some awesome warm hats. I prefer wool pilot caps like those sold at Polarn O Pyret (there are 2 stores in NYC). They are not crazy thick so they layer well and will last you into spring. A new baby will be "froggy style" (legs tucked in/under) in most any baby carrier you use for the first couple of months anyway, so I don't think you need to stress about ultra warm clothes for a newborn in the the carrier.
If you plan to use a stroller, then again, the bundle me is the most convenient nyc option. You can use a blanket, but it's just harder to keep it covering the baby in a cozy way. With DD, I chose to put her in a bunting once she was mobile in winter, because we were always stopping off at playgrounds and I wanted her warm while playing. But that won't be an issue for you till next year.
Anywho - I think the most important thing to remember is that spring weather will arrive in NYC when the baby is still very tiny. Before you know it you'll have a 6 week old and the April weather will be warm and lovely. It's always a nice idea to have a range of clothing options, but I don't see much of a need for any out of the ordinary winter wear for a March nyc baby, except for a thin wool pilot cap and maybe a bundle me cover if you plan to transport baby in a car seat frequently.
I know that lists are helpful sometimes with this stuff - here's what I'll aim to have on hand that should fit when baby is born (due March 9, we now live in Chicago so weather is a bit colder than NYC):
3 cotton hats
2 cotton pilot caps (hanna andersson and polarn o pyret)
1 wool pilot cap (polarn o pyret)
1 warm fleece hat
4 cotton gowns
5 cotton long sleeve onesies
1 wool onesie
1 pair of cotton footed pants (might get another pair - i like under the nile brand)
3 or 4 pairs cotton pants will cuffs on the legs (hanna andersson wiggle pants are my fave. i also like polarn o pyret)
1 or 2 cotton footie sleepers
6 cotton short sleeve shirts
2 cotton cardigans/sweaters
6 pairs warm, well-fitting socks
1 pair swedish moccasins (heavy socks with leather soles, you can get then at h&m or hanna andersson)
1 lightweight fleece bunting
5 swaddle blankets
3 pairs baby leg warmers
(i personally prefer baby gowns and pants with shirts or dresses, as opposed to one piece outfits.)