To put it simply, cold wallet is a wallet that is not connected to the internet while hot wallet is. They each have their different purposes but generally it is advisable to store your crypto in a cold wallet if you are not planning to trade it often as that is a safer option compared to storing it on a hot wallet. Exchange wallet is typically a hot wallet. Basically, a hot wallet is analogous to a current account while cold wallet is similar to a saving account.
Storing your funds in a cold wallet prevent you from being hacked but you will have to be responsible for the physical storage of your fund. Note that saving your fund in a cold wallet doesn’t mean that your fund is automatically 100% safe. You might lose access to your funds due to physical damage, malfunction or misplacement of the storage medium.
Types of cold storage includes:
1.Paper wallet
2.Hardware wallet (e.g. Trezor, Ledger Nano S and KeepKey.)
3.Data storage medium like a USB or Hardrive
4.A bearer instrument such as a physical Bitcoin