Not 100% sure, but I believe so. I poked through the settings and preferences for a bit and didn't see anything remotely for changing the save location.
Yeah, you will need to reinstall steam. However if you just download and reinstall steam to your other hard drive, you should be able to copy your old steam folder to the new hard drive.
The folder you'll want to back up is C:\Program Files\Steam\steamapps (or where ever you currently have steam installed). By dropping this folder into your fresh install, you won't have to re-download all of your games.