I'm not sure, but perhaps they also had freighted in one of those new-fangled ammonia ice plants that chilled a brine and the galvanized cans full of water were run through it. Those had been around for about 10 years and were getting popular in places ice was hard to find.
The exact way the ice got there would be a good research project for someone with some extra time on their hands, since that ice cream parlors were around all through the west and there were a couple methods of obtaining ice, I think there are more important things for me to research.