Car/truck batteries are made for high amp discharge then quick recharge, the battery is only there to start the engine
Alternator provides ALL vehicle power at minimum 13.5volts after start up
Cold temps slow down the chemical reaction used generate high amps, which is why it can be hard to start an engine in cold weather
But just sitting in cold temps shouldn't effect a disconnected battery as long as it doesn't freeze
A 50% charged battery won't freeze until temp is below -50degF or so
Fully charged -75degF
Trickle charging causes electrons to be exchanged between plates in the battery, this does keep it warmer but also increases the chances of a short between the plates, and you get a self draining battery
I would disconnect one battery cable for storage, and leave it
If you want to put a charger on it then do it a few days before you will be needing vehicle again, if you want
I agree with this. Cold doesn't affect a battery that is not in use (infact, the battery will probably last better stored in the cold than where it's warm because cold lowers the rate of self-discharge).
I have six vehicles that don't get driven much. Three of them are usually outside all the time. I keep them all plugged into trickle chargers, even the ones that sit in the shop where it never falls below 50 degrees... many times it has been the difference between jump starting a truck or just getting in and it fires right up. The batteries last a lot longer too - I can usually get 7 or 8 years out of a battery, sometimes 10 or more. I bought the AGM battery in my '86 in 2012 and it's still going strong.
Speaking of, if you have AGM batteries, it is extra important to keep them topped off. My experience with them is that if you have a slow draw, there will be a point where they get just low enough and short out and drain down to nothing very quickly. At that point they cannot be revived and are junk. The ones I use in my Explorer from Carquest have done that several times, they will sit at right around 12-12.5v for months and then crash to nothing overnight if you don't either trickle charge it or drive it once in a while.
I've experienced that with pretty much every type of lead-acid battery, not just AGM...
What happens is, if a battery sits at anything less than 100%-charged for a prolonged period, over time the lead sulfate on the battery plates starts to harden. When it hardens, it becomes non-conductive (and is why a badly-sulfated battery behaves much like an open circuit).
Fully recharging the battery returns all the (unhardened) lead sulfate back into it's lead and sulfuric acid constituents. Once hardened however, the only way to revive it is with a special pulsating (desulfating) charger (and that's only if the sulfate is still attached to the plates... If it flakes off and falls down to the bottom of the cell (usually the result of impact or vibration), then the battery is done forever).