Well, I'll just go ahead & throw in my opinion and our family's preferred method (actually, it seemed more like a strict rule to me when I was growing up):
Cold apple pie got a wedge of good Cheddar
Hot apple pie got cream of some sort
I was far too small ever to glean how, why, when, where this started. My father joined the Army Air Corps in 1942 to go fight the Nazis in his B-17, and then come home. But instead, he stayed in, a career Air Force officer for nearly 30 years. He, and we, traveled the world, picking up bits and pieces of far flung ideas and customs. So, somewhere along the way, he was served hot apple pies and cobblers and tarts and crumbles and Brown Bettys and strudels with cream/ice cream. And somewhere was served the same apple pastries, but cold with Cheddar cheese.
He just couldn't give up either.