My experience with writing is that it's often a matter of simply noting down what comes pouring from my subconscious, with the most taxing task being keeping ahold of some given connection, sentiment, or wording (as that subconscious seems to generate more than my working memory can keep track of).

Sometimes I struggle to fit those sentiments and connections to wording that I imagine will make sense, to someone else or even to myself. I guess that would be the, "Writing is thinking," part, but it seems more like, "Effective and coscientious (self-)communication is thinking."