It is possible that certain APIs such as for the Monero Twitter feed could be a possible security threat. Although any APIs that are added to the wallet will be believed to be safe by the developers that implement them, the safest practice would be to disable APIs that you will not be using. In the case of Twitter, its API will be disabled by default.
The first line of defense: use a secure operating system. This means no Windows, no running random binaries (except below), and keeping patches up to date. If you know how to use them, use VMs, and do all risky stuff on VMs, not the host.
When you've done that, backup your wallet/seed, use a complex password for your keys file.
Could I just delete the Monero GUI wallet and wouldn't it just go back to being cold?
You could delete it and it would become kind of "cold", but if it was "hot" at any moment in time, then during that time you were exposed to the risk of leaking your wallet file / password / mnemonic to some adversary if your computer was compromised at the time you made ...
Yes, your view wallet is hot, but that is safe. Even if someone gains access to your computer, he can not steal any funds because the view wallet doesn't store your secret spend key (which you have written on the paper backup).
Cold wallet with the spend key doesn't have to be a different computer. You could use the same physical computer, and boot from ...