Can you add methods to node-entities?
I believe I have found something that does what I want: https://www.deeson.co.uk/labs/extending-entitydrupalwrapper

The basic idea is that, since drupal-core doesn't facilitate the extension of entity-classes, we use the entity-metadata-wrapper instead. 

The above example would then be reformulated as such: 

class MyNodeWrapper extends EntityDrupalWrapper{
    public function __construct($data) {
        parent::__construct('node', $data);
    }

    public function sayHi(){
        drupal_set_message("Hi!");
    }
}

function myNode_entity_load($entities, $type){
    if($type == 'node'){
        foreach ($entities as $entity) {
            $emw = new MyNodeWrapper($entity);
            $emw -&gt;sayHi();
        }
    }
}


This appears to be a very reasonable approach. Only thing I dislike about it is that you can't use entity_metadata_wrapper to get the MyNodeWrapper-wrapper.