would it be more secure to transfer them to a hardware wallet
Yes.
Many times, major exchanges go bust are hacked or founders disappear with the money. Cryptocurrency exchanges are not well regulated despite what many claim. There are no government safety nets for investors and creditors of cryptocurrency exchanges.
The risk with a cold wallet is that you fail to make backups, fail to store a recovery phrase in physical form in a separate location and fail to make provision for family to recover money should you become unable to, through illness, injury or death.
