Depends whether its wet and if wet with what water. If you washed it out the last time you used it then you might have some water in the BCD and it would be best not to freeze it. TBH I would have thought that stored at home, dry and warm would always be better anyway, even for the cylinder where condensation in cold weather could make any surface rust issue worse.
I agree with Mr Bosun, the most important criteria is whether it was left wet or dry. Leaving kit on board (in a locker) that's wet, maybe sea water in a cold environment with little/no airflow can't be a good thing. I'd suggest that you bring it home...............better still, while you're not using it, send it away for a service!
mmmmm, think i'll bring it home, just its so blinkin heavy and just when you need it its not on board. Suppose vice versa when it needs to be at home its not....maybe i will keep them all in the van but then sods law the van will get nicked!
Apart from the weight belt in the lazaret all my dive gear is stowed below decks. All the gear has been washed and dried prior to stowing. I don't have a wet suit as we're in the Med.
I wouldn't leave a DV in a cockpit locker over winter or a stab jacket for that matter.
I do not know about the temperatures but I guess that the damp will have an effect on the bottle rusting. Better keep it in the dry? Especially if you need them testing for Nitrox?????
Leaving your dive gear in a damp wet potentially freezing environment is not conducive to long term reliability. If you are diving we all know how important it is to have reliable gear and I know how I care for my kit so that it looks after me!
Take the 'soft' stuff home to the warm and dry, especially the regs, BCD and wet/dry suit. Weight belt and tank are fine in the boat, providing the tank has a decent dry fill in it. External rust on a tank is not much of an issue; it's inside that's the problem and the colder it gets, the slower any reaction will be anyway.