Q:

Best OS for cold storage

I want an OS which can be easily disconnected from all hard drives (just uses USB) and can be booted from usb stick, also secure enough and disconnected from internet by default (or something I can easily disconnect from Internet forever). 

A:

Use TAILS Linux.  From the website:

Tails is a live operating system that you can start on almost any computer from a USB stick or a DVD. 
It aims at preserving your privacy and anonymity, and helps you to:

use the Internet anonymously and circumvent censorship;
  all connections to the Internet are forced to go through the Tor network;
leave no trace on the computer you are using unless you ask it explicitly;
use state-of-the-art cryptographic tools to encrypt your files, emails and instant messaging. 

Even Edward Snowden uses it.