Tree

struct node;

struct edge{
    node to;
    char letter;
    inline friend bool operator < ( const edge &a, const edge &b ){
        return a.letter < b.letter;
    }
};


struct node{
    set <edge> edges;
    int val;
    node( void ){
        val = 0;
    }
};

How to make this work?

What you are asking about is called "mutual class definition". Here are a couple of sites that present a solution to your problem:
http://www.codeguru.com/forum/showthread.php?t=383253
http://photon.poly.edu/~hbr/cs903-F00/lib_design/notes/advanced.html#CyclicTemplates

I think the latter is the best one. Try something like this:

template <class Graph>
struct edge {
        typedef typename Graph::node node;
        node to;
        char letter;
        inline friend bool operator< ( const edge &a, const edge &b ) {
                return a.letter < b.letter;
        }
};
template <class Graph>
struct node {
        typedef typename Graph::edge edge;
        set <edge> edges;
        int val;
        node( void ) {
                val = 0;
        }
};

What about a dynamic list? How can I create a "node" somewhere in memory and save only a pointer of it to some variable? Of course, I don't want that node to disappear when a function closes.