Here in the Queensbury/Glens Falls area, we have a couple locally legendary hot dog joints (Dog Shack and New Way Lunch, which has been around since 1919). They both cook their dogs on a griddle and the dogs are skinless.
There are a couple great hot dog joints down near Albany and they, too, griddle their dogs.
If one goes up north to the Plattsburgh/Malone areas, hot dogs seem to be steamed most places. Other than the places who serve Glazier's red hots (super snappy red skin), I think most places use skinless dogs because the focus is more on the Michigan sauce.
I don't think I've ever been to any place who uses charcoal for anything, let alone dogs.