When a Sunday falls on December 31 of any year, licensed restaurants and hotels authorized to sell alcoholic beverages under § 3-3-210 may automatically sell alcoholic beverages for on-premises consumption between the hours of 10:00 a.m. on Sunday and 2:00 a.m. on the following Monday unless the city, town, or county establishes by ordinance a lesser period of time within which alcoholic beverages may be sold for on-premises consumption by the licensed restaurants and hotels.