When you say the "northeast of the US," you can mean two very different areas as far as water temperature, assuming we're talking about the ocean. South of Cape Cod, Massachusetts, the water is a lot warmer than north of Cape Cod. This is a direct function of the Gulf Stream. Water in Maine, and further north into Canada, is extremely cold, and even in the summer won't make 15 degrees Celsius in a lot of places. Swimming time is measured in minutes. In winter, survival time can be less than a minute.
However, with training and a plan, you can actually stay in for a while and make it work. Immersion approaches can help, such as wetting yourself down and rubbing yourself, letting your skin become used to the cold water. I find this works reasonably well, but a man's balls are going to try climbing back inside him once you go into the water. Another approach, which I've never tried, is rubbing yourself with grease as an insulator.
I go sailing into November and occasionally capsize. A wet suit, a plan on what I'm going to do, a life jacket, and training work well and I figure I can stay in the water for about 15 minutes without a problem, although I won't be happy. This is a sudden immersion, but I've never had the automatic gasp or anything like that. But even though this is a sudden immersion, I'm mentally prepared for it to happen.
With proper planning, it's very doable to swim across a cave, even with water in the 5 degree Celsius range.
Jim Clark-Dawe