Set does have an iterator method; this is used internally by the for-in loop syntax. However, it does not implement the Iterable interface.

This notably means that new methods, like String.join, do not work with Sets, even though they have the iterator method.

As far as the documentation is concerned, I suspect that it's not documented because Set doesn't actually implement the Iterable interface. In other words, it's an internal method.

You'll also notice that other methods are not documented, either. For example, Object isn't documented, despite having two methods you can use (equals and hashCode).

I'm not sure you'd get a better answer short of having a real salesforce.com employee posting an answer.

There's no notion of Object.getClass() in Apex; the alternative is using instanceof with a known set of types.

Below is modified handler that uses JSON.serialize, then determines whether ofAnyType is an array, object, or some other primitive.

Assuming an array (either a Set or List in Apex), it can be cast to List<Object>. This can be iterated over to determine the instanceof for each member.

An alternative implementation would use ofAnyType instanceof Set<Object_Type_Here>, though is not as abstract.

public static void handler(Object ofAnyType)
{       
    String jsonString = JSON.serialize(ofAnyType);
    System.debug(jsonString);

    // if array, use List<Object>
    if(jsonString.length() > 0 && jsonString.startsWith('[') && jsonString.endsWith(']'))
    {
        List<Object> mapped = (List<Object>)JSON.deserializeUntyped(jsonString);

        // iterate over mapped, check type of each Object o within iteration
        for(Object o : mapped)
        {
            if(o instanceof String)
            {
                System.debug((String)o);
            }
        }
    }

    // if object, use Map<String, Object>
    else if(jsonString.length() > 0 && jsonString.startsWith('{') && jsonString.endsWith('}'))
    {
        Map<String, Object> mapped = (Map<String,Object>)JSON.deserializeUntyped(jsonString);

        // iterate over mapped, check type of each Object o within iteration
        for(Object o : mapped.values())
        {
            if(o instanceof String)
            {
                System.debug((String)o);
            }
        }
    }
}

For quick testing, I saved handler in my StackTesting class. You may use the code below to execute anonymous Apex and see the results.

Integer i = 42;
Set<String> strs = new Set<String>{'hello', 'world'};
Set<Object> objs = new Set<Object>{'hello', 2, new Account(Name = 'Sure')};

StackTesting.handler(i);
StackTesting.handler(strs);
StackTesting.handler(objs);

Note that a more robust implementation would make use of Pattern within Apex, which would take place of the .startsWith and .endsWith for determining whether jsonString is an array or object.