Leave alone the Save-data that's kept in your My Documents folder. 99% of the time, the gamesaves you find in that folder are never stored/removed by the game's installer. Rather, that data is actually generated when you run the game itself. When you boot up a game for the first time, it places config files and userdata there... that sort of thing. The core program files/binaries will be kept in the programs folder though (obviously).
If you uninstall BF3, I'm guessing it won't remove your gamesaves unless there's a specific option too. BUT... you should probably back them up just in case anyway.
As for moving the game itself: I'm at work right now, so I don't have Origin running. But I think it's just a matter of:
1. Copying over the main BF3 program folder to the place you want it
2. Uninstalling BF3 through Origin
3. Install BF3 again, but change the install directory to the new location where you moved the program files.
Origin should automatically recognize the program files already stored there, and it will complete the install process within a few seconds (much faster than if you were to re-download the game completely). I hope that helps.
Source: I reinstalled Windows on my SSD a few weeks ago, but kept BF3 stored on a secondary HDD. I re-install Origin and simply pointed it to the pre-existing BF3 files to get it working again.