Can I spend/transfer bitcoins directly from cold storage?
Every bitcoin and bitcoin transaction is stored in the blockchain which is online, distributed and known by every full bitcoin node.

What you have on your pc are private keys.   As long as you have this private key, you can sign any transaction which matches the corresponding public key.  

An offline, or cold-wallet is a wallet that is not connected to the internet, so nobody can ever figure out your private keys by hacking you - the keys aren't connected to the internet.

Spending coins is basically signing (with your private key) that you wish to yield the control of your coins to someone else.

To sign this message, you will usually need a pc which is online to create the message to sign, and has a copy of the private key.  It also needs to be online to send that signed message.

So unless you have a way to transfer the message to sign to and from a completly offline computer, you will always have to bring your wallet online to spend your coins...