When a gas is subject to less pressure, heat is absorbed. Thats why compressed air or C02 chills when let out rapidly. and what makes airconditioning work. I would think that the seawater is being chilled somewhat. Is there any data as to the temperature at the well head leaks?
At the leaks, it's obviously cold enough to freeze escaping CH4--isn't that what was causing the crystals? I have no idea, but lighter gases are freezing down there. I don't know what you're thinking, but there's no way to freeze the thing shut, for several physical reasons.
The water is near freezing at that depth anyway. The reason the coffer dam did not work is because the compressed methane gas in the oil is expanding and freezing after it combines with the water. And the well oil/gas is not nearly as cold as the water to begin with - I thing maybe 200F or so? It still would end up absorbing a lot of heat from the water if it's starting out 3000PSI over the surface pressure. It has a mile of water to cool off on the way up, but I can't imagine that amounts to much when you consider all the heat in the Gulf water to begin with.
I am sure you are technically correct, but the solar heating effect of the sun will make that a non issue. The surface temp of the Gulf in summer is about 90 degrees ! A little cooling could not hurt it and will not be noticed. What is a potential problem is that as the volume of natural gas increases, and violent lightning storms are a trademark of the Gulf in summer, there could be explosions in the area where they are working.