The most direct way is probably to install an ssh server on the windows box. Cygwin includes an ssh server.
Depending on how precise your timing needs are, you might be able to have an "at" job on the windows box that runs periodically (every 5 minutes?) and runs if it sees that a particular file exists, deleting the file. Then you could use Samba/smbclient to create the file. You would need to turn on filesharing on the windows box for this to work.
If the windows box has a web server, you could write a CGI, and trigger it using wget or cURL.