slytherin_petra It is safe to move the Sims 3 user folder (the one in Documents > Electronic Arts) to an external drive, or to move the Electronic Arts folder. It is NOT safe to move the entire Documents directory to an external because Windows could react badly if the external were ever disconnected, either physically or in software, and any program called for access to Documents.
Moving the folder is a simple matter of cut and paste, available when you right-click. Getting the game to actually read the folder on the external requires a symbolic link. I can help with that if you let me know which folder you'd like to move and what the file path to the new location would be. For example, you might move the Electronic Arts folder to a folder called Sims Data on your D drive, in which case this would be the file path:
D:\Sims Data\Electronic Arts
You can of course also install the game on the external drive if you want. You'd need to uninstall it where it is now and reinstall, but you wouldn't need a symbolic link. Just tell the EA App to install the game where you want when you click Download. It's best to create a folder on the external so you're not installing directly on the drive, e.g. D:\Games\The Sims 3 rather than D:\The Sims 3.
Having said all that, Sims 3 would load much more slowly when on an external drive. Gameplay would be the same, but any loading screen would be longer, as would starting the game and entering CAS, and saving for that matter. An external HDD's read and write speeds are likely much slower than what your internal drive is capable of, and with the amount of data being processed, that makes an obvious difference.
So if you have anything else you could move to the external instead, that would be the better choice. Even Sims 4 is less affected than Sims 3 unless you have a massive cc collection.