gewoon de Private Key invoeren?
Yes.
A paper wallet is not actually a wallet, but a backup of your wallet; for instance, if your hardware crashes, you lost the password of your actual wallet, etc. Then you could use a paper wallet, to restore your actual wallet. Or, like you did, adding it to your other wallet(s).
And one should keep their paper wallet very safe, because it contains the private key. If someone knows that private key, they can restore that/your wallet into any compatible client.
"Cold storage" is anything considered an alternate address (or multiple ones) you're not actively using, and being in some form that can either be disconnected or never make contact with the internet; like a hardware wallet (Trezor's), a usb-drive, a paper-wallet, etc. A 2nd PC or laptop or even a phone with a wallet installed on them (but with different address(es) than that you are actively using) can be considered as cold storage devices.
Though a cold storage device (in any form) doesn't need to or possibly ever can come in contact with the internet, the address and transactions themselves always will (provided, the cold storage is actually used to store something on it). That's simply how the blockchain, the ledger, works: One can indeed generate a cold storage option which never ever connects to the internet, but in order to store something on it, one need to broadcast those transaction(s) on the network.
Cold storage is cold storage. You can store anything you want in it/them; so long as it's main purpose is to not being your active address and to store things on them, even though the address and transactions would have to be "exposed" to the internet, it still remains a cold storage device