Owning bitcoin in a cold wallet is like holding 100-year old preferred stock certificates in Ford in your safe. No matter what happens to the stock market, your claim is still valid.
This analogy addresses the fears of "what if the internet goes down?" or "what if they shut down the miners?". No matter what happens to the network today or tomorrow, your proof of ownership is preserved behind 256-bit elliptic curve digital signatures. The bitcoin network is primarily a transaction processing and validation system.
For self-audit purposes, possession of secure private keys plus a validated copy of the blockchain showing an unspent output spendable by those keys is sufficient to be certain of one’s bitcoin holdings, independent of current network availability.