Cold wallets are not limited to hardware wallets, it's simply a broad term to describe wallets which are meant for cold storage, in other words assets sent there are meant to be stored for the long term, preferably offline (hardware wallet or airgapped device). They can always receive transactions as it does not require internet connection, but should ideally only send out once.

Hot wallets are wallets which are used actively for sending and receiving, example would be a trader's account on an exchange.