How did/do the Russians make carrot tea?
You use the leaves, not the carrot themselves. I don't know for sure this is what your Russian Civil War book was talking about, but I know it works, and besides, if they were desperate enough for acorn coffee and carrot tea, I imagine they were eating the carrots. This site suggests that you might need 1/4 cup of carrot greens per 1 cup of water; you can find plenty more searching for "carrot top tea".