We're experiencing the exact same problem since upgrading to Snow Leopard. When the students attempt to save to their Windows 2003 home directories the file saves but instantly becomes "read only". They then aren't allowed to save, only 'save as' with a new name. Additionally, if they attempt to open another document on the server it too becomes read-only. Furthermore, if they save to the desktop and then drag and drop into the server, they get a permissions error. However, the file does actually copy to the server, despite the error.
Using Open Office fixes this issue. Open Office is able to save to the server without any issues.