On all the cruises I've been on (7 - some new boats, some very old) this has never been a problem. I've never, ever been too hot if anything cold and there has always been an adjustment to turn the air down.
I live in the South and like a very cool room, too. I'm one of those "64 degrees works for me!" people. Never had any problem with the A/C on a ship until a Holland America cruise last May. The thermostat just plain didn't work, so they brought in an enormous floor fan that took up half the cabin, but did the trick. I usually found it a bit cool in the dining rooms, though. I was always the only one at a table for 8 without a dress jacket or sweater on. Three Carnival cruises, and no problems with the A/C.
darlenejake, I found the room very comfortable and quite cool when we got back from dinner. I also like it cold but had to turn it down at night or you freeze. You can adjust it any way you like it on the newer ships