Without traveling far you could make it in just about any time of the year.
The recipe is simple ~ first prepare a large shallow pool. Fill it with water to the depth of half an inch or so.
Make sure you do this in a very dry part of the world that has exceedingly clear skies, e.g. Iran, Iraq, Saudi, most of North Africa, etc.
In the morning, just before dawn, when everything is at it's coldest, soop up ice crystals from the top of the pool of water.
Place them in an insulated container and protect them from the Sun.
The secret here is that the heat in the water will radiate through the clear atmosphere out into space. For much of the year this will allow a degree of cooling sufficient to produce ice on the surface.
Folks in more Northerly climates, e.g. Anatolia, or up in the mountains, would save winter ice in springhouses.
BTW, having read through several translations of the Koran and having consulted with several highly educated mullahs, I find nothing that says that ice is forbidden to Moslems. The idea that something that didn't exist in Mohammad's day is prohibited is simply BS concocted on the spot for the purpose of killing people or stealing their businesses. It's a "con".
You have just described the origins of Islam.