Many here are suggesting that they do not keep anything on exchanges. I doubt this. They must be having good amount on exchanges. They operate with huge amounts and must be involved in trading crypto also. It will not make much difference to their net worth even if they loose funds on one exchange due to hack. They keep the risk versus reward ratio in mind before taking such decisions. Keeping the money idle in hardware wallets or paper wallets will give them no returns at all.
It is difficult to know the Bitcoin storage conditions of corporates, but i am sure that Bitcoins stored in very large quantities will not be kept on online exchanges. Cold storage comes to mind as the most secure means of Bitcoin storage. This is because private keys stored in an internet connected wallet are vulnerable to network based theft. Cold storage solves this problem by signing the transaction with private keys in an offline environment. But there is a catch. Since bitcoins stored in cold wallets will take time to transfer to online exchanges, i think it will be difficult to buy and sell in sudden situations. For such cases, they can store bitcoins in online exchanges, albeit in small amounts, with special methods.