To answer the current meaning or meaning of the question: Is the possibility of making ice with modern equipment?
It is all about what you’re calling “modern apparatus”. Refrigeration was first commercialized in the early 1850’s using equipment that isn’t described as “modern”. It was still difficult to find in the past and in an agriculture society in remote areas (specially pumps that can create an atmosphere of vacuum or compress gases) however, it is not impossible.
The most straightforward method to create ice is to make alcohol evaporate by forcing it to evaporate with the help of air. This method is based on the similar principle that was employed by the Romans however, using an even more powerful working fluid.
Quotes From refrigeration:
The year 1758 was the time Benjamin Franklin and John Hadley, professor of Chemistry in Cambridge University, conducted an experiment to investigate the idea of evaporation as a method to quickly chill an object. Franklin and Hadley confirmed that the evaporation process of highly volatile liquids such as alcohol or ether can be employed to lower the temperature of objects beyond the point at which water freezes. They conducted their experiments using the bulb of mercury thermometers as their subject and bellows for “quicken” the process of evaporation. they decreased temperatures of the bulb down to 7 degrees Fahrenheit (-14 degC) in the midst of an ambient temperature was at 65 degrees (18 degrees Celsius). Franklin observed that shortly after passing the point at which water freezes (32 degF) the thin layer of ice grew on the outside of the thermometer’s bulb . Franklin also noted the ice layer was approximately a quarter-inch thick at the time they ended the experiment when they reached seven degrees Fahrenheit (-14 degree Celsius). Franklin concludedthat “From this experiment, it is possible to think of freezing a person into death during a hot sunny day”.
However, this isn’t an efficient method, since the alcohol that is consumed is more valuable than generated ice.
The following is an answer to the original wording of the question:
Is it possible to make ice without electricity?
Certainly.
Refrigeration doesn’t require electricity by itself*. Therefore, a civilization does not need an understanding of electricity in order to build refrigeration. If you look through the background of refrigeration, it was used industrially prior to the time that electricity networks became readily available.
The two most popular methods currently in use include vapour compression refrigeration that is used in fridges in the home and in the vapour absorption method of refrigeration. The first requires mechanical effort (a pump, usually driven through an electric motor) and the second is an energy source that is thermal.
Theoretically it is possible to connect the pump of your refrigerator to any non-electric source of mechanical energy (an engine, windmill, or even an source of power from humans like pedals) it will continue to create refrigeration. In the real world, when electricity is not available, reliable, or is not readily available The second option that is absorption refrigeration, is utilized, using the waste heat, fuel as well as solar energy.
See:
Refrigeration
Absorption refrigerator
——————-
* excluding some fringe applications like magnetic refrigeration and thermoelectric. Even then the electricity required can be created on site for this particular case: James Dyson Award | Jamesdysonaward.com