Your wallet by default retrieves wallet and blockchain info from your roaming file. You can configure this in settings.
If youre using it for cold storage spending, then you don't need the blockchain. Just copy the Bitcoin data file without the blockchain folder into your HDD and change the path in your Bitcoin client settings, and youre good to go.
For cold storage so you can plug it into your computer in the future and resync it from where you left it, you can keep the blockchain but you'll need sufficient storage. Honestly by the time you plug it back in youll have multiple gigabit web transfers as a standard, so it won't matter