Exchange private keys. No way to get out of it?

[A.Wolf]

I'm new to bitcoin and I still can't find a clear answer to my doubt.

If I buy bitcoins on an exchange which won't disclose my private keys, it means I can't send the coins to an address of, say, my electrum cold wallet?
Is this the case? I would be forced to sell and buy only within the exchange? 
If so, how can I use my coins for something else than trading or investing? 

The next question is, is there a list of exchanges that disclose your own private keys?

[TryNinja]

If I buy bitcoins on an exchange which won't disclose my private keys, it means I can't send the coins to an address of, say, my electrum cold wallet?

Yes, you can. But not directly like you would with a wallet you control. All exchanges will let you ask for a withdraw of your coins, which will be sent to the address you choose previously.

Is this the case? I would be forced to sell and buy only within the exchange?
If so, how can I use my coins for something else than trading or investing?  

You will see a withdraw page with instructions on how to request your coins.

The next question is, is there a list of exchanges that disclose your own private keys?

No.

[Coin-Keeper]

There is some good reading at localbitcoins dot com.  Transfer of coins from your wallet there to an Electrum wallet is fast and safe.

[zoomzoom]

It's cos the coins, in a lot of cases, aren't really in your wallet when in an exchange, only when depositing to, and withdrawing from the site, are the actual wallets used, this to avoid fees. I think the site would be reluctant to give out keys for wallet associated with you as they would lose fees from it.

[CoinFalcon]

Most exchanges will not give you access to the private keys for simplicity reasons but as soon as you move them to a wallet such as bitcoin core, you will have access to them.