The governing body of each county may adopt ordinances effective in that portion of such county not embraced within the corporate limits of any incorporated town, and the governing body of each city and town may adopt ordinances effective in such city or town, prohibiting the sale of wine or beer, or both, between the hours of twelve o’clock p.m. on each Saturday and six o’clock a.m. on each Monday, or fixing hours within such period during which wine or beer, or both, may be sold. Such governing bodies shall provide for fines and other penalties for violations of any such ordinances which shall be enforced as if the violations were Class 1 misdemeanors, with a right of appeal pursuant to § 16.1-106. Such ordinances shall not affect the sale of wine and beer on common carriers of passengers by train, boat, or airplane. A copy of any ordinance adopted pursuant to this section shall be certified by the clerk of the governing body adopting it and transmitted to the Board. On and after the effective date of any ordinance adopted pursuant to this section, no retail licensee authorized to sell wine or beer, or both, shall sell or permit the drinking of wine or beer on the premises of such licensee during the hours limited by the ordinance.