Hi Steffen,
That opens the message in a browser, but on my system, not in a new window.
I think that function is built into mu4e already and all you need to do is have:
(add-to-list 'mu4e-view-actions '("ViewInBrowser" . mu4e-action-view-in-browser) t)
But your email made me review the existing functions, and on my OS X system w/ Chrome (running usually on another virtual desktop), I can now get a new browser window on my current desktop with the following code:
(defun kdm/mu4e-msg-view-action-view-in-browser (msg)
(start-process "~/path/to/Google Chrome.app/Contents/MacOS/Google Chrome --new" nil "~/path/to/Google Chrome.app/Contents/MacOS/Google Chrome" "--new")
(sleep-for 1) ; may need to increase this
(browse-url (concat "file://" (mu4e~write-body-to-html msg))))
(add-to-list 'mu4e-view-actions
'("View in browser" . kdm/mu4e-msg-view-action-view-in-browser) t)