Thanks to Craig and Adi's work, we now have tests sort of working on appveyor. However, they aren't actually reporting their pass/fail status right now as github statuses, I am assuming because of the persistent failures that were causing noise on unrelated tickets.
However, it's very close to being a useful builder; there are really only 2 remaining issues, not counting turning on the reporting itself. I've made an umbrella ticket here:
https://twistedmatrix.com/trac/ticket/8664 and documented what's wrong with each one.
So, if you care about Twisted on Windows, fixing the issues documented there should make it much easier for more folks to contribute easily :).