When I do
C-c C-e h o the file opens in an Emacs buffer instead of my default browser which is odd because org-mode links do open in the browser as is the case when I preview a file from web-mode, so Emacs must know how to open the default windows program for html files.
I have tried to customize the
org-file-apps variable as per an answer in this question. I put in the cygwin path of browser executable and org-mode now indeed opens the browser but the browser fails to open the file as Emacs gives it a cygwin path to the html file, and I don't know what magic I would have to insert to convert the file path to a windows one. In any case it should open the browser with default setting for this variable, which was default before I changed it.