I've been flying at night in the GOM for a few years now, and I have a few observations.
Deaths from exposure are non-existant. If you do go in the water, it's not that hard to survive if you have a life vest, and exposure suits are simply excess baggage. You don't die quickly from 80 degree water.
Night flights aren't all that common, but there are a significant number of single-engine flights at night compared to the overall number. There are a few operators flying single-engine at night over water.
Given the choice between single-engine or single-pilot ops, I'll take single-engine every time. A second pilot is far more important than a second engine. Engines don't quit that often, especially turbines, and if they do, a reasonably competent pilot can get the helicopter down safely enough to get everyone out. What kills people is flying into the water inverted, hitting obstacles on landing, flying into thunderstorms, etc. A second pilot is, IMO, far more important than a second engine, and should be required for night flight whether over water or over land. Night EMS single-pilot flights will continue to kill people, as long as they are permitted. Night flight single-pilot flight anywhere will kill people. If I flew single-pilot all the time, I wouldn't be writing this, I would be feeding the fishes. I don't care if you have one engine or three, if it's dark or IMC you need two pilots active in the cockpit, and night flight will eventually become IMC, guaranteed.