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There are two kinds of wallet hot wallet and a cold wallet. Ideally, people keep minimum balance for trading in a hot wallet and most of the coins are stored in cold wallet. I am wondering why coins in the cold wallet are not tradable?

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The very point of a cold wallet is that it's less easily-accessible to provide additional security guarantees. By storing and interacting with your private keys offline, there is a smaller attack surface for bad actors trying to gain access to your private keys. By removing that friction, you're making that cold wallet a hot wallet by definition.

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The word "cold" describes that activity of the account. Or more accurately, the lack of activity. No activity - it's cold.

Hot, being the opposite, meaning there is activity.

In the context of crypto wallets, a cold wallet is a wallet that has its private key(s) stored in of the following fashion:

  • Air gapped machine (no internet access)
  • Paper wallet (printed private key)
  • Hardware wallet
  • Any medium that is not easily accessible

Without access to the private key, one cannot send ether or tokens out from that account. They can, however, receive ether or tokens as only the wallet's public address is needed to be the recipient.

TL;DR: Private key is needed to send or trade tokens. Cold wallets do not have an easily available private key to sign, or approve, outgoing transactions.

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Actually, coins on a cold wallet machine CAN be traded ( I'm talking about a dedicated computer here). A transfer can be generated on a connected machine, giving a transaction ID, basically a large number. This can be transferred by some medium to the airgapped machine with the cold wallet (a QR code is the most secure way). You then sign the transaction with your private key and generate a new, signed code. This signed code is transferred back to the connected machine which then broadcasts the transaction to the blockchain. It's secure because your private key never leaves the cold wallet, which is airgapped.

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