Hardware wallets are offline wallets. It means they are not connected to the Internet when you are using them to make transaction.
This is incorrect. Although you can use a hardware wallet offline, most users connect it to an online computer. Ledger nowadays can even "call home" and
send your recovery phrase to Ledger.
Ledger is a cold storage wallet.
It's not. Cold storage means the device is never connected to the internet.
Even if you connect it to an online device, it will not reveal your seed/private keys.
That's not true. You need the read the link I posted above!