Hmm... I found a Win2k server (with IIS 6) which I could use for testing and set up the webdav support by following these instructions:
(or well, I didn't change the NTFS permissions so the folder was writable by anyone.)
I then configured Rainlendar's Network Shared Calendar plugin to use the server's webdav folder and after few (expected) 404 errors the ics file appeared to the folder and I was able to use it without any problems.
So, I have no idea what could cause the 403 error. Perhaps the webdav works different way in IIS 5?