If its a reputable exchange, then probably they are taking care of the security measures like moving your assets to cold wallet etc.. I have been dealing mainly with Polo since feb 2016 and I still have allot storred in BTC there, never had an issue ever with them, smooth withdrawals with zero problem when transferring to Node wallet.
It doesn't matter how reputable an exchange is when it comes to them having control over your funds ~ we've seen how reputable exchanges have turned into a scam in a very short time.
In most cases there are the first signals that are pointing at a change in how the exchange is being operated, but you can't always depend on these initial signals to warn you for an exchange that might turn into a scam.
And btw..... People nowadays have been going through quite some difficulties with Poloniex, and for that reason made a switch to Bittrex. If I was you, I would directly withdraw every coin from there that you don't trade with.
Don't expose your coins to unnecessary risks.