Yes, HTTP-Only cookies would be fine for this functionality. They will still be provided with the XmlHttpRequest's request to the server.
In the case of Stack Overflow, the cookies are automatically provided as part of the XmlHttpRequest request. I don't know the implementation details of the Stack Overflow authentication provider, but that cookie data is probably automatically used to verify your identity at a lower level than the "vote" controller method.
More generally, cookies are not required for AJAX. XmlHttpRequest support (or even iframe remoting, on older browsers) is all that is technically required.
However, if you want to provide security for AJAX enabled functionality, then the same rules apply as with traditional sites. You need some method for identifying the user behind each request, and cookies are almost always the means to that end.
In your example, I cannot write to your document.cookie, but I can still steal your cookie and post it to my domain using the XMLHttpRequest object.
XmlHttpRequest won't make cross-domain requests (for exactly the sorts of reasons you're touching on).
You could normally inject script to send the cookie to your domain using iframe remoting or JSONP, but then HTTP-Only protects the cookie again since it's inaccessible.
Unless you had compromised StackOverflow.com on the server side, you wouldn't be able to steal my cookie.
Edit 2: Question 2. If the purpose of Http-Only is to prevent JavaScript access to cookies, and you can still retrieve the cookies via JavaScript through the XmlHttpRequest Object, what is the point of Http-Only?
Consider this scenario:
- I find an avenue to inject JavaScript code into the page.
- Jeff loads the page and my malicious JavaScript modifies his cookie to match mine.
- Jeff submits a stellar answer to your question.
- Because he submits it with my cookie data instead of his, the answer will become mine.
- You vote up "my" stellar answer.
- My real account gets the point.
With HTTP-Only cookies, the second step would be impossible, thereby defeating my XSS attempt.
Edit 4: Sorry, I meant that you could send the XMLHttpRequest to the StackOverflow domain, and then save the result of getAllResponseHeaders() to a string, regex out the cookie, and then post that to an external domain. It appears that Wikipedia and ha.ckers concur with me on this one, but I would love be re-educated...
That's correct. You can still session hijack that way. It does significantly thin the herd of people who can successfully execute even that XSS hack against you though.
However, if you go back to my example scenario, you can see where HTTP-Only does successfully cut off the XSS attacks which rely on modifying the client's cookies (not uncommon).
It boils down to the fact that a) no single improvement will solve all vulnerabilities and b) no system will ever be completely secure. HTTP-Only is a useful tool in shoring up against XSS.
Similarly, even though the cross domain restriction on XmlHttpRequest isn't 100% successful in preventing all XSS exploits, you'd still never dream of removing the restriction.