Can you help me understand how a cold wallet works?

Thank you advance for clicking my dumb post and reading this.

So I understand these:

1. You only need to plug in the cold wallet to transfer OUT BTC from the cold wallet
2. You don't need to plug in the cold wallet to transfer IN BTC to the cold wallet

I'd like to know how the above #2 point works. If I'm transferring BTC from an exchange to my cold wallet address, how does my offline cold wallet know it received BTC? It is sent to a specific address (cold wallet address)... just like an exchange address... What is the point of having this physically?

Thank you for your time to answer my stupid question.

p.s. Currently using ledger nano S Plus