Well to be honest I can test my code in IE9 to see if it works. But I have no idea how a disabled person is experiencing my website, I do put all the "alt" attributes etc...but it's hard to imagine it.
Yes, that's a real issue. I've had to add JAWS Screen Reader support to an app, and even after you shell out for the thousand dollar license, it's very difficult for a casual user to use it in the same way that an actual blind user does. Ideally you test with an actual impaired user, but they have real jobs and don't want to spend all their time testing your apps.
Besides others mentioned, Sim Daltonism is a good OS X app for testing how an app or page's color choices will look with various forms of color blindness.
Color Oracle is a cross-platform app for the same purpose, though I haven't used it much, yet: http://colororacle.org It seems rather good in my limited testing.
Colour Contrast Analyzer is a Windows/Mac app for testing whether text/background contrast is sufficient. This is a matter of both color and brightness - a color combination that looks fine for a normally-sighted user may he completely unreadable for others for a variety of reason. (Part of why everyone's suggesting designers avoid the gray-on-gray or light-gray-on-white design hipster crap.)