So the process goes like this?
Deposit funds into exchange, they go to a cold wallet
Confirm withdrawal
Multisignature confirmation from exchange
Funds move to hot wallet
Withdrawal transfer is made
Is that right?
I think most cold wallet funds are manually accessed, and kept away from that process you mention. Deposited funds typically are swept up periodically (you can see this on explorer, every so often your deposit address funds are spent into another address and is usually left empty), depending on size of output. You can see some cold storage wallets of exchanges in the top 100 wallets.
Bitfinex's cold wallet shows only a handful of txs a day
Hot wallets are probably continously funded by deposits and automatically process some withdrawals... liquidity as TryNinja points out.
Quoine claims to be a 100% cold wallet exchange, and indicates it's likely the only one to make that claim.
I'm pretty sure every exchange has some liquidity in their hot wallet, so they don't need to keep pulling coins from their cold wallet every time someone wants to withdrawal.
Absolutely. It would simply cost too much, in terms of not just time and human resources but risk. Cold storage is supposed to be what it suggests. Storage. Accessing it multiple times just makes it too exposed, too vulnerable... if not to malicious attempts of theft, then of carelessness.