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I just want to understand what actually they store in the cold wallet because all bitcoins anyone owned is already in the blockchain.

Do they store the private key of users in cold wallet?

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Do they store the private key of users in cold wallet?

In short, yes. (Some) private keys are stored in cold wallets.

The record of all bitcoins (UTXOs) exist as a public database, which is stored in full nodes all around the world.

To spend a UTXO (ie, some amount of bitcoin), the user must be able to produce a valid signature, by using the appropriate private key for that bitcoin address/script.

Those private keys are stored in various ways. One such way is a 'cold wallet'. Generally, a cold wallet describes a way of storing a bitcoin private key, such that the device storing the private key has not, and will not, connect to the internet. Conversely, a wallet that exists on an online machine is usually referred to as a 'hot wallet'.

There are also different types of hot wallets, and cold wallets. But the online/offline distinction is the main distinguishing factor.

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I think there's some confusion about what "in the blockchain" means.

The blockchain contains information about how many coins belong to which addresses. But if you want to actually spend the coins from a particular address, you have to sign a transaction using the private key for that address. So yes, what's stored in a wallet (hot or cold) are private keys.

If the private key is lost, the blockchain will continue to remember about the coins that belong to that address. But nobody will ever be able to spend those coins anymore, so they're effectively lost.

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Do they store the private key of users in cold wallet?

Usually, no.

As you mentioned, the actual bitcoin balances are evaluated from data stored on the blockchain.

A common system is a user wallet, hot wallet, and cold wallet system. For personal use, the user wallet is omitted.

Companies will store the keys to all the user wallets on a secure server. When someone deposits BTC to their user deposit address, it will be moved to a cold wallet address.

A hot wallet is used to process withdrawals, and usually contains a small % of the company's total BTC holdings. They keys to this wallet are also on some secure, but online server. In an ideal set up, user and hot wallet keys are stored inside an HSM device.

A cold wallet is simply a collection of addresses for which the private keys are not on an online or easily accessible device. This can be a paper wallet in a safe, a hardware wallet, or an air gapped machine. The general idea is to prevent key exfiltration or arbitrary signing of transactions.

A cold wallet will contain the majority of the funds. By doing so, a company can limit their loss to the contents of the hot wallet + user wallets in the event of their online systems being compromised. Compromising a cold wallet will usually require physical access to the keys in some form, along with some additional knowledge to decrypt then (a hardware wallet PIN, safe combination, full disk encryption password, etc.)

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