For light cleaning a waterless or rinseless wash will work, but if your car sees more substantial grime (assuming it does since you're in NY) I'd have to side with the guys who suggested taking a couple buckets to the local coin op.
You'll have salt and road grime to deal with that will simply be too much for a waterless washing product to knock out safely and you'll want to also be able to blast those things from the underside of the car, rocker panels, fender linings, etc with some kind of pressurized water (from a hose or a pressure washer). The less you touch the car while its really filthy and the more of the contamination you can remove before you take any towel or mitt to it the lower your chances of introducing swirls or other damage.
You might find this helpful if you decide to go the coin op route: