From Binance to Coldwallet

Hello,

I’ve taken advantage of the dip in the last couple of days and bought Bitcoin and Ethereum on Binance since I’ve seen that a lot of people were recommending this app. Now I’ve read a couple of things were people were complaining about Binance and the high fees or that Binance even stole coins out of their wallet. Apparently you don’t “own” the coins on Binance so I’ve thought about putting them into a cold wallet since I was just planning on holding on to them and buy more during dips. How would you proceed from now? Should I just leave them on Binance or should I switch the trading platform? Thanks a lot for any help in advance!