You want to be careful how literally you interpret that 2 degrees (sea water of 'normal' salinity.) One of the funny effects with salt water is brine concentration. Initially, it's not the salt and water that freezes, but just mostly the water. A little bit of the water freezes out, leaving most of the salt behind in the remaining liquid. So as more of the mixture is solidified, it's possible to get pockets of water of increasing saltiness and decreasing freezing point.
Now in a reg, I imagine the situation gets even more complicated, with different amounts of circulation at different places allowing some of that excess salt to be dumped back into the surrounding ocean, or droplets getting into 'air' parts of the reg, where they have the opportunity to completely freeze over with loosing salt, and how big a lump of ice (microscopic or not) it takes to be a problem.
BTW, I *think* that commonly referred to 2 degrees is Celsius and not Fahrenheit.
Enough scientific philosophizing for one afternoon.