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Will a cold storage wallet always work? What happens if the bitcoin protocol is updated? Is there a vulnerability in the protocol that could be changed to create this situation? Where is this formally documented?

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There's a page in the wiki dedicated to Bitcoin's weaknesses. Specifically there's a section which describes what would happen if the cryptography would break. Linked is a forum post by Satoshi:

If the hash breakdown came gradually, we could transition to a new hash in an orderly way. The software would be programmed to start using a new hash after a certain block number. Everyone would have to upgrade by that time. The software could save the new hash of all the old blocks to make sure a different block with the same old hash can't be used.

In any case I do think that eventually it will become obsolete and you will have to transfer your funds to more secure public/private key pairs. Like Satoshi said, SHA-256 is very strong and could take several decades to break.

On a positive note, the transition will be gradual and the community will have time to alert people about the change. This means that you'll have the time to eventually upgrade the keys in your cold storage.

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There is no formal documentation for Bitcoin apart from the Wiki and the code itself which is now heavily commented.

To answer your question, no. However it may become insecure which is different from becoming obsolete.

A future iteration of the bitcoin protocol may require you to move your coins from one address (inside a wallet) to another more secure one.

This situation could occur if a weakness was found in the current security of the algorithms used in Bitcoin, and, by general agreement, everybody decided to upgrade to a new set of secure keys. You would be foolish not to do the same even if you had not touched your cold storage for years.

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Cold storage is a general term for private keys that are kept disconnected from the internet. It can be a paper wallet, it can be a computer that is not and has never been connected to the internet. It can even be an engraving on a ring. So you won't find any formal documentation of "cold storage" anywhere. Actually you won't find formal documentation of anything related to Bitcoin but that is something else.

If what you mean by obsolete is amounts you hold in any type of cold storage to be spent without the physical means being destroyed or stolen, then no, they cannot be obsolete.

But your paper wallet can burn, your computer hard drive might get broken and you might end up not being able to spend the bitcoins you were holding there. If that's what you mean, then yes they can be obsolete.

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