Using developer tools, I can amend a css file for a site I'm currently viewing in a browser.
I want to, effectively, do the same - but instead of amending the css file, loading a local css file, just for that particular domain.
Another way of phrasing it: "When any page of stackoverflow.com is loaded, load C:\test.css to the browser".
Yes, it's possible. Have a look at http://userstyles.org.