At an annual or special meeting a town may vote to exempt for a period not exceeding five years at a time real and personal estate used and occupied for hotel purposes. When a majority of those voting on the question of such exemption at an annual meeting vote in favor thereof, such vote shall not be valid unless it shall appear that the total grand list of such majority is equal to at least one-half of the total grand list of those voting on such question. When a majority of those voting on the question of such exemption at a special meeting vote in favor thereof, such vote shall not be valid unless it shall appear that such majority is equal in number to one-third of the total number of legal voters in such town, nor unless it shall appear that the total grand list of such majority is equal to at least one-half of the total grand list of those voting on such question.