I've frozen a few soups in my time. I like to use a gallon ziplock baggie, and will pour maybe two quarts into the bag, and freeze. Being in a bag that big, if you lay it flat, it's rather thin, and thaws rapidly.
If you freeze a soup with potatoes in it, when you thaw and reheat that soup, that potatoes will have a mealy, grainy texture, but will taste OK.
I've got some Posole in my freezer right now. I'm wondering if the hominy will also have a mealy texture.
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