Definitely in places like Arizona, it might be a problem, because the moisture would build up quickly inside along walls, air ducts, things like that. As far as New York, you guys aren't in a desert. I would think you wouldn't have too much of a problem. Like others have stated, just watch your windows, walls, etc. If you have moisture buildup then it's too humid and you need to open a window and let some moisture out. It all just depends on the relative humidity outside in regards to how high you can keep the humidity inside. For example, it is currently at 58% humidity inside my house, and it feels awfully dry in here (to me), so I will be adding some moisture into the environment (Air Conditioners create a drier environment, and it was 95 degrees yesterday, so we are using AC). Our humidity outdoors is currently at 91%. So, I could easily add moisture and bump our humidity indoors to around 85% to 88% and have no problems and no condensation issues or worries. As a side note--I will not be making it that humid in here.
I do have humidifiers (cool air) that I use in the winter, because the heater dries everything up so much. If my 2 humidifiers aren't keeping up because the furnace is so hot, rather than buying more humidifiers, I just boil water on the stove. It puts moisture into the air and it also raises the temp. in the house, so it's a win win.