Quite the opposite, to my understanding. Heat does more permanent damage to batteries than cold. While cold will deplete a battery, it can be fully recharged. An overheated battery will lose recharge capacity over time. This has been shown to be the case in electrical vehicles.
Well, permanent damage includes freezing and cracking. I’ve never had that happen in the summer. 
We were over a hundred degrees for over a hundred days this year - much of it above 105.
Phoenix and Las Vegas were worse. Your summers like that?
Yes, heat damages the battery, but does not kill it. More batteries die in the winter than in the summer. This is why you see batteries advertised as being able to “handle the cold” much more than being able to “take the heat”. Yes, resistance to heat is important, but they die in the winter.
Last battery I had that died was on a day of -40C. 
Your winter’s like that?
From here - How Hot Weather Affects Your Car Battery - Consumer Reports
Car batteries typically last from three to five years, according to AAA, spanning from 58 months or more in the furthest northern regions of the U.S., down to less than 41 months in the most southern regions. Inspections should be part of an owner’s routine maintenance, but it is especially important to check before taking a long road trip.
The C is redundant.
That’s funny, I forgot -40°c = -40°f.
@Northern_Piper I live in Cold Lake, AB and regularly see those winter temps. A battery for me typically lasts 5-6 years. When I replace them, it’s generally with the largest capacity cca I can stuff into the battery holder so I can squeeze every last revolution out of the motor when the tires are square. 
At -15C your battery is providing roughly half its rated capacity so a battery weakened by a typical scorching Prairie summer is going to have lost some of its electrolyte to evaporation if it’s a typical flooded cell type battery. That’s why AGM and spiral grid batteries like the Optima can be a good thing but they have their own set of issues.
Everything you’d want to know… BU-201a: Absorbent Glass Mat (AGM) - Battery University
“As with all gelled and sealed units, AGM batteries are sensitive to overcharging. A charge to 2.40V/cell (and higher) is fine; however, the float charge should be reduced to between 2.25 and 2.30V/cell (summer temperatures may require lower voltages). Automotive charging systems for flooded lead acid often have a fixed float voltage setting of 14.40V (2.40V/cell); a direct replacement with a sealed unit could overcharge the battery on a long drive.”
This is why I mentioned charging profiles if you switch to AGMs in your car upthread.
The battery doesn’t die in the winter - the chemistry just slows down. If it’s been previously compromised by hot summers, when you put it in the deep freeze it might not be able to give you the amps you need - but if you warm it up again, it’ll come back to life. But nobody wants to wait for warmer weather in the hopes that their battery will once again become useful; they (quite sensibly) replace it on the first cold day that leaves them stranded.
The End of It
Shop said battery was worn out with only 1/3 of its CCA ability left, and replaced it. All the rest of the electrical system including the alternator check out fine.
Short lived battery, but good news everything else was fine.
WooHoo!
Batteries do die in the winter. You are correct that the chemistry slows it down. A battery that is very cold may not have enough charge to start your car because if the cold. You can warm the battery up and it will be able to start it, but you can also kill the battery. If you run it down trying to start your car, It might be able to be recharged, but it is also likely that it will no longer hold a charge, ie, dead. If you had warmed the battery up and recharged it before draining it, it might have lasted another year, but using it in the winter is what killed it.
Hot summers kill batteries, but they die in the winter.
They used to be. Born and raised in Wisconsin.
Actually, -40C and -40F are the same. The scales converge at that point.
I don’t do F.
So you’re saying you don’t give an F.