From my understanding, many free web hosting companies do not allow certain types of files on their servers to prevent people from storing them.
However, it is a great idea to use free hosting providers to test things out, see how they look, play around. While there are a lot of stable providers, it is difficult to find them. If you do, however, find them, I would highly suggest performing active backups of your data to help protect against any kind of information loss. The last thing you want is to work on a new site, have it done the way you want it and then provider going down or out of business.