There are exceptions, of course. You can still draw samples of different colors to let the user choose one, and icons and other images don't need to be changed. You can also continue to draw color samples in the colors they represent rather than drawing them all in standardized colors. Similarly, most icons and other images can be drawn in their normal colors. But again, if you have monochrome versions of these images, you should use them when the High Contrast mode is on.
Many applications let the user select independent colors for a number of different purposes.
In most cases it's fine to display these colors instead of those specified through the Control Panel. However, keep in mind that Windows also provides a keyboard shortcut to turn on High Contrast mode. Because of this, standard UI elements such as menus and dialog boxes should be drawn using the appropriate Control Panel colors whenever the High Contrast flag is set. The application must provide documented keyboard access to all features. The upshot is that the user should be able to use the product effectively without having to rely on a mouse.