It has nothing to do with the web host, I was just using it as an example, because free web hosts use forms to upload files (the ones that are too stingy to let ya have ftp!)...
Word allows you to open multiple files, yes, but these don't. To upload multiple files, you'd have to have it log the filename etc. for each file, and the file contents, so they just don't do it.
The best way is to put multiple boxes, or find a java applet (I'm sure there's gotta be one available somewhere, but I don't like Java so I never looked!).