I like this idea, but I don't think it should be anything too conspicuous, because the fact that you've already voted to close something already isn't something that's entirely important (in comparison to the rest of the information on the page) until you've actually opened the dialog.
I'm not sure if this is just a design change, or a functionality change, because whether you specifically voted to close the question might not be loaded with the rest of the page and may only load after the dialog has loaded.
On the other hand, though, I'm pretty sure it's the former, because that information does appear to be loaded with the rest of the page, as is indicated by the tooltip:
For that reason, I think it should be simple (and subtle) enough to change the default font color to
#444 (the current hover color for buttons) to indicate that you've already voted to close:
I don't like the idea of changing it to something like dark red or
#888 (the color for disabled buttons) because it indicates that you can no longer perform any actions with that button (which is obviously false).