How to best hold wild rice
Wild rice, if left in the soup, will absorb water until it is bloated and mushy.   You should therefore refrigerate it separately, and add it as you are finishing the soup.

Foxes, deer, raccoons and so on aside, assuming the temperature outside is at 40 F / 4 C or lower steadily, you can use it as a giant fridge/freezer.  Of course, if the temperate goes as low as you have indicated, your soup base is likely to freeze, which may be inconvenient.