Cold Cuts is definitely a northeast thing, and not just NY. Not going to lie though... Lunch Meat is kind of dumb. Why "Lunch" Meat? Can you not eat Cold Cuts for dinner or even breakfast (if you're weird enough)?
in Pittsburgh Lunch meat is the meats you get at the grocery store and put in your fridge when you get home Cold cuts are are the made sandwiches from those meats sold at delis/sub shops
Both are acceptable, I'd say "Cold Cuts" is more of a group of sandwiches while "Lunch Meat" is what you have in your fridge at home for a snack