It isn't so much how cold it is on the ground as how cold and moisture-rich it is higher up. I once witnessed (from the window beside my seat on the plane) a "manual deicing" at PSP a few years ago. The ground staff literally came outside and took brooms and large blankets to the wings because that's all they had available. The pilot explained that as the plane had come in to land, it had come down through clouds laden with ice crystals, and it wasn't warm enough on the ground (about 40 that day) to melt the ice quickly enough to get us out of there.

So if it can happen in the desert, it can certainly happen at LAX!