Hot storage is a wallet that is accessible online, eg, n wallet used by the "bank" to transfer coins from their own account to a customer that wants to be paid out.
A cold wallet is one where the keys are kept offline and not plugged into anything, eg, a printout, or a USB key.
If they secured their servers (from hacking), they could theoretically leave everything in hot storage (although it's not necessary for normal operations as others have stated).
A cold wallet is one where the keys are kept offline and not plugged into anything, eg, a printout, or a USB key.