Question

I want something that provide:

std::list head;
std::list::node node;
while (node = head->next) {
    do something with this node
};

It is rather weird to me that a list does not have a next pointer.

Answer 1

The actual implementation of the list is hidden. Since the standard dictates the the insertion and erasion of an element at a given position should be possible in constant time we can assume that something like a node is going to be used:

23.3.5 Class template list [list]

23.3.5.1 Class template list overview [list.overview]

A list is a sequence container that supports bidirectional iterators and allows constant time insert and erase operations anywhere within the sequence, with storage management handled automatically. Unlike vectors (23.3.6) and deques (23.3.3), fast random access to list elements is not supported, but many algorithms only need sequential access anyway.

However, the important thing about C++ container is that they all provide the same interface to actually traverse the content: iterators:

for(std::list<double>::iterator it = list.begin(); it != list.end(); ++it){
   *it += 3.0; // add 3.0 to each element
}

If you think about the list as a C-style object with

struct node{
    struct node * next;
    struct node * prev;
    double value;
};

struct list{
    struct node * first;
    struct node * last;
}

the loop above is somewhat equivalent to

for(struct node * it = list.first; it != list.last + 1; it = it->next){
   *it += 3.0; // add 3.0 to each element
}

However, things like it = it->next are hidden in the actual implementation of the std::list::iterator. Since they provide an almost* unified interface for all classes you should learn to use them.

* Some do actually provide a little bit more functionality than others, for example RandomAccessIterators vs. BidirectionalIterators, but this is something you will learn later.