How did/do the Russians make carrot tea? A while ago I read a book about the Russian Civil War (it was Blood on the Snow by Emanuel Litvinoff) in which the characters frequently drank coffee made out of acorns and tea made out of carrots. I tried naively making carrot tea by grating some carrots and pouring hot water on them, like I would make ginger tea. But the resulting brew did not taste strongly of carrots.

How is carrot tea brewed--what part of the carrot is used? I would also be interested to know whether there are any other countries in which this has ever been a popular drink.
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".