I don't know how hardware wallets function, I thought the only thing that makes a hardware wallet different from a hot wallet is the security side of things and also keeping the wallet offline.
Cold wallets are effectively the same with hot wallets in the wallet design, what makes it different is how it is used.
A Hot wallet is connected to the internet and used for making regular transactions. They are more exposed to online threats.
Cold wallets are not connected to the internet, but 'frozen' offline away from any threat online.
A cold wallet could be a hardware or software wallet, ensured that it is not connected to the internet. This wallet could vary in its specification like number of seed words.
- Jay -