Hi, sorry I didn't see this till now. I suffer from caper obsessive disorder (an annual condition, but it's stabilising out and I only collect about twice the amount I need in recent years, rather than 10 times, like I used to). And I also grew up in New York state, and now live in a place where capers grow wild.
The good news for you is, where I live now, at high altitude in the Himalayas, has similar temperature winters to downstate New York where I grew up. Minimum temperatures of -10 to -13F (-23 to -25C), and 6 to 8 weeks of
pond skating.
But the bad news for you is, it is very very, .... verrrrry.... dry here. I don't know how capers would like the humidity and precipitation of New York. Here, if we get a rainy summer, which means maybe a total of 5 rainy-ish days in a month, a lot of the wild caper plants get some kind of powdery white mildew. It only happens once in five or 10 years here.