There is a few ways to do this probably, but I think the fastest way to set it up is with an FTP server on the Linux box and the ncftpput command. You can get the ncftp client here for Windows:
Its included with Linux. Just zip or tar up the files, and use cron on Linux and AT on Windows to schedule the jobs. You could even use cygwin on the windows boxes so that the scripts are all the same regardless of the platform.