In England in Victorian times and before (and probably in other countries too) not everyone could afford the luxury of delivered ice - and anyway poorer people could only afford to shop for the bare necessities every day and these got quickly gobbled up by the much larger households of the time! What people needed was a safe place to store food overnight or until mealtime. This was usually called a 'cool pantry.' The pantry was often located on the coldest (North) facing wall of the house/cottage, and often had a tiny window high up. This window was often protected by a sort of metal sieved screen to keep the flies out. On the inside, the walls where shelved, and on the shelves were kept perhaps a jug of milk or cream, cheese in a specially shaped china wedge, perhaps a ham or other cold meat,rashers of bacon,a pot of butter or a few slices of cold pie or brawn. The cooler temperatures in there would have been enough to keep the food cool for 2/3 days (we probably wouldn't risk it nowadays!)
People did preserve their foods via pickling or salting, yet the most practical (if it could be afforded) was the ice box in areas that could sustain it. I am from New York and there are actually a lot of old houses that still have ice boxes outside and even what you could call ice silos, very tall structures meant to hold more than one block of ice as a back up.
This link has a very basic picture of an icebox and explains, pretty well, how it worked.
There were a few different ways of keeping food before refrigerators.
Most recently (just before modern refrigerators became very common) people used iceboxes. These were like refrigerators but instead of being cooled electrically, they were cooled by having actual ice in them.
Before that was available, people had cool cellars and some had ice houses where ice could be stored (under sawdust, often) and kept cool for much of the year. These places could keep some food cool.
But mostly, in those days, food was preserved some other way -- by smoking it, salting it, or drying it.
Just before the refridgerator, people used insulated ice boxes. The "ice man" travelled from the ice house with blocks of ice either in a large truck or in a horse drawn wagon. He grabbed the blocks of ice with huge sharp tongs and swung it into the ice box. When the family wanted ice, they had to chip what they needed with a super sharp pick, called appropriately an ice pick. They also dried, pickled, canned, smoked and salted meat and vegetables to preserve them.
Refrigerator is a device to artificially cool substances below the surrounding environmental temperatures. Before people had refrigerators, mostly they used nothing instead of them. That is people did not try do any thing to cool things below surrounding temperature. They just managed without such cooling. However a device that can cool water a few degrees below the surrounding environmental temperature has been in use for thousands of year. This is the humble earthen pitcher, which cools the water by evaporation of the water seeping out of the small pores in the pitcher wall material.
Also when faster means of transportation developed, people used ice brought from cold regions to keep things cool.
When it comes to method of food preservation rather than refrigeration it is worthwhile noting that that are many methods of food preservation other than refrigeration, and use of these non refrigeration type of food preservation has also increased in recent times rather than decreased with use of refrigerators. The only difference is that these methods of preservation are adopted by large manufacturers in the process of manufacturing packaged food items, rather than by individual households. For examples earlier jams were earlier made by housewives, but now these are mostly made bu big companies and sold as packaged food products.
You are asking a question about something that I can sort of recall. In the old days when food could not be preserved people used to smoke it or bury it deep in the ground. Ground temperatures are cooler than above ground. Of course sometimes animals dug up what people were trying to keep, so that led to other methods. If people lived near streams some would try and preserve foods using water.
People started building cellars or well houses. Well houses were deeper than cellars and often cooler. Wines are still kept them in some areas. People later used them to store ice and would place food in the new ice cellars.
The things that I recall were called ice boxes. They had a metal box on top of a metal box. Men came by (on a horse and wagon where I lived). They would drop off blocks of ice that were placed in the top part. Later the box was moved inside the ice box. Eventually the boxes changed into freezers when the advent of electricity became a reality in every home.
By the way, I can remember when milk containers were delivered to our door by horse and wagon and the milk was packed in shaved ice.
they had this seller underground and they would put cold water or snow and put there wine under there and it would keep it cold and the door would be so small so the coldness woul not get out