Batteries do not operate well at low temperature. The chemical reaction in the battery is slowed by low temperatures. So if you attempt to use a cold battery it will tend to appear to discharge quickly but it actually is a slow down in the chemical reaction occurring. OTOH, a fully charged battery will hold a charge longer if it is cold for the same reasons.
If you want to use the battery it is best to keep it room temp but if you want to store it charged then colder is better. I do not think permanent damage will result from freezing temps.
Your other hardware is probably not so temperature dependant. As for
juice, I have seen people say to keep it room temp and I have seen people that store it in the fridge or freezer. Not sure what to tell you here, but I keep mine at room temp.