Some of us know that when the engine is cold and the OAT is below 20c then you will need about two shots of the primer ,as the OAT drops more priming will be required untill with an OAT of -5c you will require a mimimum of 6 shots of the primer.
I see no reason to crank a cold engine on a cold day when the battery is at its least capacity just to prove what I already know ......the engine wont start without priming.
Most instructors try to teach this to the students so to save running batterys flat and over using starter motors but the bit that is usualy poorly taught is the use of the checklist .....see my post above !.
The advice in the flight manual is not practical advice based on years of starting engines , in is a get out writen in by the lawyers to get out of claims that are the result of overpriming or slow starting after priming.