If I do not to want to create a new container in order to do so?
You can't iterate through a stack or a queue. In fact, SGI's documentation says this (it's about stack, but it's the same reason for queue):
This restriction is the only reason for stack to exist at all. Note that any Front Insertion Sequence or Back Insertion Sequence can be used as a stack; in the case of vector, for example, the stack operations are the member functions back, push_back, and pop_back. The only reason to use the container adaptor stack instead is to make it clear that you are performing only stack operations, and no other operations.
So, if you really want to do this, you'll have to empty the stack (or queue):
std::stack s;
// ...
while(!s.empty())
{
Whatever w = s.top();
std::cout << w;
s.pop();
}