FLA will be fine without the need to remove or insulate provided they are stored pretty much fully charged. I suspect AGM will be the same as FLA.
FLA will not freeze as long as they have a decent charge, I suspect AGM will be simular.
Now if you are planning to use them during the winter, then insulating them to keep them a bit warmer will help some to keep cold weather capacity loss a bit less. Extreme cold temps reduces effective capacity in both cases.
For straight out storage, you do not need to insulate or keep them warm, just charge them to full, then disconnect the batteries from the house completely making sure you do not have any small phantom loads which will drain the batteries.
FLA can easily handle extreme cold weather stored in sub zero temps without freezing provided they are charged and as long as there is no other low power drain will easily go 6 months or more without the need for a top off charge.
AGMs are pretty much the same other than they have a much lower self discharge rate and can go longer between top off charges during storage.
Of course if you have shore power and a converter you can depend on shifting into storage mode (13.2V) you can just allow the converter to run 24/7/365.
Zero reason to remove or insulate the batteries for storage provided they are charged.. Some old habits do not die easily.
Contrary to the old wives tales, you do not have to store FLA batteries on wood to keep them off the concrete floor either..