It turns out, (some) nomadic herders literally eat nothing else, at least for parts of the year. Other parts of the year, they will suplement their diet with some grains or other imported items. Here are first hand accounts from William of Rubruck in ~1250 and here is one from Nikolai Przhevalsky in 1870.
Some choice quotes from William,
Nevertheless, in summer, so long as lasts their cosmos [Ed: a fermented mare's milk, usually spelled kumiss], that is to say
mare's milk, they care not for any other food.
In winter they make a capital drink of rice, of millet, and of honey,
; it is clear as wine : and wine is carried to them from remote parts.
For a more substantial meal the Mongol mixes dry roasted millet in his cup, and, as a final relish, adds a lump of butter or raw sheep tail fat (kurdiuk).
Another useful quote from the second article concerns modern practices:
When the Russians pulled the plug on Mongolia’s aid in 1991, the economy went into a severe crisis. For many Mongolians it was their first experience of serious hunger. The staple traditional diet of meat, milk and flour saw many people through this crisis. Mongolians traditionally have turned to foods that are high in protein and minerals, relying less on more seasonable foods like vegetables and fruits. This means a diet heavy on meat and dairy products, the latter when sour in the summertime thought to clean the stomach.
While by modern nutritional standards, a diet of all milk and meat isn't super healthy, it was all the Mongols ate during the summer, and most of their diet year round. Keep in mind that milk does a have a lot of sugar in it, so from cows milk at least, you get more calories from carbohydrates than protein from milk. I guess that was enough to conquer most of Asia.