The National Weather Service issued winter storm watches for six New Jersey counties on Saturday afternoon in advance of a coastal winter storm that could hit northern parts of the state on Tuesday with 6 to 12 inches of snow, while much of the region could see a wintry mix or heavy rain along with high winds. The winter storm watches include Hunterdon, Morris, Sussex, Warren and the western sections of Bergen and Passaic counties. The earliest watch takes effect at 6 p.m. Monday in Sussex County, which could see 7 to 12 inches of snow. The rest start at midnight Tuesday or soon after. Sussex …