A wallet does not hold coins; it holds the keys that let you move them on the blockchain. Hot wallets are connected to the internet and convenient. Hardware (cold) wallets keep keys offline. Lose the seed phrase and the funds are gone; no one can reset it.
Trading on a dex requires a wallet. Holding on a cex means the exchange holds the keys.
Example: moving 2 BTC from an exchange to a hardware wallet removes exchange counterparty risk and adds the risk of losing your own backup.