"why can't root change the ownership of this folder?"
The VFAT file system has no provision for ownership or permissions. So Linux fakes ownership and permissions by giving every directory and file in the mounted VFAT file system the same ownership and permissions as the mountpoint. You can change the permissions for everything in the file system en masse by changing /mnt/windows but you cannot change individual files or directories within the file system mounted on /mnt/windows. Also I think that you have to umount /mnt/windows before you can change its permissions and then remount it.
Be prepared. Create a LifeBoat CD.