Hardware wallet can be used anywhere?
Hardware wallets are easy-to-use ways (compared to paper wallets (hard to use) and software wallets (not as safe as hardware wallets)) of being in control of your private keys hence the safest and the easiest way of using and storing cryptocurrencies.

When you use a (traditional) exchange as a wallet, you won't be in control of your private key so the exchange can steal your funds or get hacked and lose them etc.

There are decentralized exchanges where you don't need to deposit your funds (thus you don't need to trust, a.k.a trustless) like RadarRelay. You can use them with software wallets and some of them with hardware wallets directly. 

Don't forget that cryptocurrencies' reason of existence is being trustless, don't hand over your funds to anyone, always be in control of your private keys.