On Steam there is a different entry for MW3, that is waiting to be unlocked for installing on November 10th. It doesn't make too much sense that this different Steam Store game (with a different game id) will also open MW2's CoD HQ. I'll wait and see, maybe there will also be a way to open MW3 directly.
So with the last Steam update, the previous Call of Duty entry in Steam now launches into MW3 directly. To enter Warzone or MW2 multiplayer you will have to wait for it to start the MW2 process. It's exactly how they did it with the MW3 beta and campaign, just viceversa, so to play MW3 MP and Warzone (starting in December) you won't have to wait for game switching.