Thanks very much for all your helpful replies - now I know a bit more about
why I've been asked to pull the prop through, and just what's going on engine-side when I do, which is what I was after
Thanks for the bedside reading, Peter
Good tips on priming and use of electric flaps in cold weather, too... what I tend to do is lower the electric flaps for the pre-flight check but only retract them once I've started the engine. I may modify that and not touch them at all in very cold weather until after the engine is running.
I am very reluctant to recommend the pulling the prop through first technique, because it can go really wrong. Mixture lean is no assurance that it will not start. Done with great care, and a correct technique, it can be helpful, but I treat it as a technique of desperation, not the "normal" way.
With all I've read about the need for extreme care when handling a prop, I have to admit this is very much uppermost in my mind, but the instructor is adamant (I've nagged him about it twice) that the engine can't start with mixture set to lean. Always assuming, of course, one remembers to check the mixture before touching the prop.
Technique? Nope, haven't been shown that...