Stomping the milk for yogurt

For variety from mutton, you could always try horsemeat, particularly popular in Western Mongolia, or roasted marmot. Marmot hunting is a traditional nomadic past time. They are killed and cooked whole, without puncturing their skin. Cooked from the inside out by stuffing with hot rocks, while fur is singed off with a blowtorch. The animal puffs up and the arms and legs extend as steam and the stones cook the marmot from the inside. It is then eaten, and washed down with mare's milk.
Extreme seasons make growing vegetables extremely difficult, so they are very hard to come by, except onions, swede, and other root vegetables that grow in harsh conditions and last for a long time. This of course makes maintaining a vegetarian diet in Mongolia very difficult, and vegetarians may find themselves living on rice and Mongolia's almost unpalatable cheeses.