While the cold does not usually 'kill' the cells (going completely dead, usually due to an open circuit), a car battery cannot deliver as much power in the cold. Power drops quite a bit, and when you couple that in with the thick oil you mentioned, a battery that would start a car fine in warm weather, just can't crank it when it gets to zero F or below.
But yes, from what I understand, the heat can 'kill' the battery. May work pretty well one day, and just dead the next.
Modern cars generally start so easily now, I feel like it's harder to tell when that battery is getting marginal. A load test is a pretty good check. Back in the 'bad old days', the car cranked long enough that you could hear if it was getting slow. Now it's usually just ... Whrr-vrooom! It used to be Whrrrrrr-Whrrrrrr-Whrrrrrr-Whrrrrrr-blam-Whrrrrrr-blam-vrooom.