You can move money into a crypto wallet without that wallet needing to do anything, or being online at all, or even having a private key that physically exists anywhere in the universe. It's just a public/private keypair; send it to the public key of a private key that's offline and it still exists on the blockchain, you just can't do anything until the matching private key comes online.

The point of a cold wallet is to keep the private key physically offline. That way you know it cannot be stolen by electronic means, because the physical device containing the key needed to authorize transactions is locked up and not powered on. Then you only power it on during very specific, audited times and conditions when it's needed to fund the hot wallet, which does all the actual automated trading and transfers.

GP's point is to have all incoming transactions to an exchange go to a cold wallet, which becomes a one-way sink, and then periodically the exchange powers up the cold wallet to sign transactions transferring assets to the hot wallet, which then funds all outgoing transactions. This isn't a bad architecture, though I'm not sure it'd save all that much here.