Most of the free hosting providers have disabled remote MySQL connections due to security issues. Even if you find one that allows remote connections, their machines usually have a lot of users (because it's free, obviously, you can't get a good service for free), so you will experience massive delays or lags on your server while waiting for the database to return results.
A much better solution would be to find a SA-MP server hosting that gives you a database along with a server. They are usually free, and if not, they are cheap. Check out the list of server hosts.