It's hard to give useful advice until you provide some critical information:

-What Zone do you live in?
-What species of bamboo?

Ditto kudzu, need specific zone an species info.

I live in New York City. I don't know what kind of bamboo it is. I got it in a NYC nursery. The leaves and stems are green. I hope this doesn't sound too stupid!

Joan-
It's not stupid. Many bamboo are as you describe: all green and hard to tell apart. It's just that there are some of these that will do fine outside and some that will defoliate or die. Without knowing the species, it's hard to give reliable advice. If you're in NYC, you're probably in Zone 6, and you probably have low temps of about 0 degrees F? How big are these bamboo? Can they be taken inside? Since you bought these at a local nursery, you may be lucky enough to have something fairly hardy, but it's hard to know. Since they're in pots, they will be less hardy than if they were in the ground. If it's possible, you should call the nursery. I suspect that a NYC nursery may not carry many varieties of bamboo and they might be able to give you a couple of species names. Then I could be more helpful.

It's probably a species of Phyllostachys (most likely "aureus" or golden bamboo). I say probably because it is a very common bamboo and I have frequently seen it sold in NYC. Then again, I've also seen Chusquea coronalis being sold in NYC (not locally hardy). You would probably have a better chance of overwintering them outside than inside. Kudsu is correct that plants are much hardier in the ground than in a contain on a terrace. NYC and close environs are now classified as solid zone 7 (0F. min). I would overwinter it in as large a container as you can get. Mulch the plant. It would also help if you provided some protection from the WIND (a tarp for example). I have successfully overwintered Golden Bamboo in containers in the NJ/NYC metro area without any damage in sheltered areas by the house. Protecting from wind is really key. Good luck!

Hi Joan. I'm new to bamboo and growing in a container as well - needed some winter interest on my deck. As the crow flies I'm fairly close to NYC. You're in zone 7, but depending upon where your terrace is located (are you upper level of a high rise? ground level protected by surrounding buildings?) your microclimate can vary.

I can only echo what njoasis said - my local nurseries gave the same recommendations. Concentrate primarily on protecting the roots first. Some additional protections could include an old blanket wrapped around the container to help insulate the roots, as well as moving the container up against a wall (preferably heated living space on the interior).

Tarping may or may not be needed (depends upon your exposure and species). I only plan on covering mine if we get sustained temps below the low 20's, mainly because my location is fairly well protected from the worst of our prevailing winter winds. I'm old school and prefer to use burlap for winter protection.

Since the species is a bit of a mystery, I'd suggest going back to the nursery where you bought the bamboo and asking the manager who does their plant ordering if they know. They really should have this info readily available even if you bought this plant in the spring.

Here's my Fargesia Rufa all potted up and in his winter home. He's been in the container about 3 weeks now and appears to be quite happy. Note that I have a good 4" of soil between the root system and the container walls, as well as a nice layer of mulch.

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njoasis,
Can't really comment on what the NYC nurseries are purchasing, but here in the 'burbs bamboos are appearing at the local nurseries. I have 3 good nurseries that I trust around here - 2 stocked F. Rufa this year, and one also stocked F. murielae and P. Nigra. I'm really hoping this Rufa does well since my plan is to move it during the summer to a location just off the deck to provide some screening/softening of an awkward area near the steps to my deck.