I have read dozens of threads saying you need to keep your BTC on a hardware wallet or paper. Anything online isn't safe they say. When trading that is not really feasible is it? I like to move in and out of positions several times a day and often at a moments notice. My trading account has a sizable balance (to me - 5 figures) in it.
How risky is this and any additional things I could do?
Read all about Mt. Gox and Bitfinex hack and look how many people lost a lot of funds in those trading platform. I'll just advise you to just enough funds in a exchange for your trading purposes and pull out most of your funds to a secure wallet. Its better to be safe that sorry. If you are willing to let all your funds then take the risk, enable 2FA and make a strong password if they planned to hack your account only. But if its a widely planned exchange hack, then nothing you can do. Its up to you dude. I hope you make the right decision.
Yes, an exchange and trading platforms are the most targeted by hackers just like you said, MT. Gox and Bitfinex are the good examples.
If you are an active traders, put your money or bitcoin in trading platform is inevitable, if it being hacked, then you are unlucky.
5 digits of money or bitcoin is big amount and must be secured, in that case just treat trading platforms or exchanges as temporarily place to do your business, in and out as fast as possible. Buy and sell and then withdraw your money, just put small amount in their wallet just in case.