Altitude is going to play some part in the answer as well.
As can be easily imagined, some mountainous parts of Colorado were well suited for collecting winter snow/ice. For the US, I think that’s about as far south as you could consistently find enough to mine.
I do not know for certain but I suspect the relatively late development of Colorado and the advent of mechanical refrigeration meant the region was never a huge supplier of ice for the rest of the country.
If Cincinnati was roughly the southern extent of ice production (I think it was a net importer because local production just wasn’t enough), then it stands to reason areas of the Smoky Mountains would be able to produce some ice for their own use. Asheville’s climate is very similar to Cincinnati’s for example, and although there’s less flat land for big ponds, there’s also shaded north slopes that get little or no sun in winter. Maybe a place like Blairsville or Blue Ridge, GA could support a small local ice industry.
I live in a suburb of New Orleans. We still have an old building known as the ice house. It certainly predates mechanical refrigeration. The ice business was big business in the South.
The Amish in my area still cut ice, and they cut it from their ponds.
You can cut the ice from a pond and it will freeze over again. One pond can produce a lot of ice over the winter.