How could people eat/make frozen desserts if there was no electricity? I get it that you can have ice and snow from mountains even in places you don't think about, but how could it not melt before being able to use it for anything? Was it a suer expensive dessert?
With natural ice! Frozen desserts are known to have existed for 2200 years, but organized ice harvests began 3000 years ago^[1]. Quick summary about frozen desserts here from the International Dairy Association^[2].
In the recent modern period, capitalists made it happen. The worldwide network of European shipping created a new opportunity for ice as an export product. In the 1830s, ice was exported from New England to India and Australia. The "Ice Trade" was responsible for creating the market demand and developing the required insulation--and those things were a necessary precursor to the first modern ice making machine by James Harrison in Australia.
And, yes. Super expensive if your country did not have native natural ice--which is probably why Australia solved ice making first.
Ice was stored in ice houses, usually insulated with straw. In the lower temperatures of summer through the 1800s (end of The Little Ice Age), it could be kept through the summer. In America, ice was cut in huge quantities on lakes anywhere the water was good, warehoused, then shipped south in insulated cars on the railroads all summer. Cars for foods needing to be kept cold had compartments for ice instead of refrigeration units.
Check the age of the icebox, the predecessor of the fridge (post ACW). The iceman delivered chunk ice to keep it cold. In summer, kids would follow the iceman's truck, begging for chips of ice to suck on for a cooling treat. The chips came from him cutting down the ice blocks he had to fit the pans in various brands of icebox.
I have made ice cream in a hand-crank unit (have a team of crankers ready): you make your custard, cool it (make it the night before if possible), put it in the can, put in the dasher and lid it. Put it in the outer bucket, and fill the space around it with ice and rock salt. The salt lowers the melting temperature of the ice! Crank until frozen, draining and adding more ice and salt as required, then pack over with more ice and let "ripen" (set up well).
Ice cream was sold by Italian pushcart venders in the streets of New York in the 1890s. Poor people might not eat it every day, but a paper cone was only a nickel. (Grace M. Mayer; Once Upon a City;: New York from 1890 to 1910; 1958; Macmillan Co, NY). "Hokey Pokey" (with some sort of mix-in) was a favorite flavor of shoeless children.
Mrs. Beeton (1861) gives for "Fruit Ice-Creams" of "Average cost, with cream at 1s. per pint, 4d. each ice."
On the other hand, one simply does not find it in medieval menus and cookbooks. I have found it in cookbooks back into the 1700s, including such favorites as Parmesan cheese flavor. No, really.