After a bit of experimentation, I discovered the following solution:
SuiteClasses suiteClassesAnnotation = AllTests.class.getAnnotation(SuiteClasses.class);
if (suiteClassesAnnotation == null)
throw new NullPointerException("This class isn't annotated with @SuiteClasses");
Class<?>[] classesInSuite = suiteClassesAnnotation.value();
Basically, it gets the classes the same way that JUnit itself gets them: by looking into the annotation and determining which values are included within it.
The category solution provided by dkatzel is also a good option if you're ultimately wanting to filter these classes, but if you need a list of classes in a suite for some other purpose such as code analysis, this is the simplest and most direct way to do it.