but it depends on the trust you give to the exchange or how reputable it is, like Binance, Bitget, and Bybit. In short, do it at your own risk.
Take note that you should not trust any exchange or custodial service with your funds, no matter how reputable you believe the exchange is. Recent events have shown that any centralized exchange can collapse and even if they don't, they could still confiscate your funds for any reason at all. Store your funds only in your self custody, back up your seed phrase in a safe location and add extra layers of security.
The thing is that, excahges are non custodial and at that, the security of funds are left in the hands of the exchanges, and at anytime the wallet onwer could lose control of the funds if the exchange feels like the operator may have violated they rules or excahge deciding to close it door on the face of the owner with all the funds in it, we have seen multiple cases of excahges becoming exit scam and with users not being able to ever recover their funds.
Much more also we have to know that when you store your bitcoin on a cold wallet, you have total control over the money and can use it at whatever time that the owner which to use such funds.
So there is a big difference between an exchange wallet and a cold wallet in terms of freedom and control of assets.