Don't worry guys, they're starting things off at 93 to 136 GB! But who knows whether the storage requirement will balloon after the third or fourth DLC pack comes out.
Activision wrote:In order to pre-load Black Ops Cold War, you must have the following free drive space on your platform:
PlayStation 4: 95GB
PlayStation 5: 133GB
Xbox One: 93GB
Xbox Series X|S: 136GB
Note: console players can choose to uninstall specific game mode packs, such as for Campaign or Zombies, in order to reduce the game’s overall file size. This content can be managed in-game through the “Account & Network” section of the Settings menu.
PC: 35 GB (Multiplayer Only) / 82GB (Full Game) / 125GB (Full Game on Ultra Graphics)
Note: PC players can also choose to install specific game mode packs, such as for Campaign and Zombies, in order to reduce the game's overall file size. Also note the updated PC file size numbers.