Only Temperate CPs. Tropical CPs do not go dormant.
Technically they go dormant every year because imagine they live in bog swams in say the US that has winter every year

You could put ice, but then you'll have to contend with putting ice every day to be sure that the temp is kept constantly low.
It depends, if you got your plants from the US, then yes it is winter now, but if you got them from Australia then it is summer now.
Well these are at least what I know
TTFN
Arvin