Cold rooms and ice houses. I was born in UK before domestic refrigerators. At home we had what was called a 'larder'. This was a walk-in cupboard on the north side of the kitchen wall that caught little sun. Inside were several air-bricks to allow for ventilation. There were two marble shelves (which are always cold to the touch), and anything needing to be kept cool was placed on these. There was also a meat-safe, a cabinet with wire sides for storing raw and cooked meats, that flies could not get into. Butter and fats were stored in earthenware over trays of cold water. Generally more foods were eaten at room temperature than we do today. Such as tomatoes and eggs, which do not need refrigeration. We lived in a city, but as a country-woman, my mother would bring home game from her visits there; mostly rabbit and hare, and these were hung, nose down on hooks suspended from the roof of the larder until ready for skinning and preparation for cooking.
Large houses built ice houses for a supply of ice. They were constructed underground and in winter, servants cut big blocks of ice from frozen lakes on country estates and these were kept in the ice house and taken to the house when needed, as aids to chilling foods in kitchens.
Other methods included salting, and from the 19th century, canning.