Kidslick! I eat deli meat both ways. If I heat it, its in frying pan or on foreman grill.
But usually cold. The big thing with me and this is a must, is to lightly toast the bread so it just turned brown. So the sandwich is never really 100% cold.
You out in New York, that gives you access to argueably the best stuff anywhere.
I am liking the munster cheese with peppers idea.