I forget the exact numbers, but basically -- a battery that's fully charged at 70F will have about 30% of rated power/current/CCA available at 0F. It's still fully charged, but lead-acid batteries work because of the chemical reaction - and that reaction goes slower at low temps than at higher ones. Another way to think of it -- if your battery is unable to crank the motor on a cold day -- and assuming you've got the time to do this "experiment" -- take the battery out of the vehicle and warm it to room temperature (which will probably take 12 hours unless you try something like a warm water bath, and be careful of heating too quickly and damaging the thing if you do so). Once you've got a warm battery -- put it back in the vehicle and it'll most likely spin the engine just fine.
A fully-charged lead acid battery won't be damaged by the cold until the temp reaches far below zero F. If it's going to be all of +15F or whatever -- there's NO NEED to put the battery in the house overnight.
I've used battery warmers to help during cold weather. They're pretty much an electric blanket -- plug into 110VAC, are 6" wide by long enough to wrap all the way around the battery, are coated with a rubberlike material that isn't harmed by leaking acid, and will keep the battery at about 50 or 60F.
Bike batteries are likely different than car/truck units -- probably because they are designed for use during warm (relatively speaking) weather. I make sure the bike batteries are fully charged if the bike is staying out in the barn -- and usually remove them from the bikes and store the batteries in the warm part of the basement during the winter. I haven't used a "battery tender" and I haven't suffered over-winter battery damage. But I do charge the batteries a bit during the off season.