Really, it would be wise to assure that the engine is warmed slowly and thoroughly before attempting to start it. This is best achieved with a plug in heater installed on the engine, and an engine blanket to insulate the engine while it warms. 2 to 3 hours should be the minimum plug in time before a start is attempted.
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.
It's not "is it going to start cold?", but, is it well enough lubricated during the start? Cold oil gets thick, does not flow well, and thus lubricates poorly. Whether you pull it through by hand, or crank on the starter, you're still moving all the internal parts of the engine with less than ideal lubrication. The pistons/cylinders are really the most difficult to damage by cold starting, least of the worries, and the most easily replaced parts, if damage were to occur. In Lycoming engines, the camshaft and followers are particularly vulnerable to wear with poor lubrication, even briefly.
I suggest that you make an effort to have the engine preheated by an accepted method, before starting it. If, when you check the oil before start, it is nice and free flowing, the engine is ready to start. If it's thick and gooey, avoid turning the engine over at all until it's warmed up. Do not direct fire into the cowls, I have seen this go very wrong too!
There are other "tricks" to warm an engine, but all more complicated, less effective, and not looked well upon in an airport environment.