Cold wallets are offline hardware wallets such as a Trezor or Ledger, which essentially act as a key to your assets stored on the blockchain, free from exploitation or hacking of your tokens.
Warm wallets are almost like hot wallets and the term is used interchangeably; they tend to be web-based applications or apps, such as Metamask.
Hot wallets is the more common term; it refers to exchange wallets that are utilised when buying/selling on an online exchange, such as Coinbase or Exodus.
Cold and hot wallets each have their pros and cons. Cold wallets sacrifice liquidity for security, whilst hot wallets do the reverse.