The cows and goats were to the nomads what farming was for the Central Plains. It certainly wasn't as though they could eat their crops or livestock as they pleased.
However, after Yan Liuyuan's arrival, Hassan had been slaughtering the tribe's goats for Yan Liuyuan to eat to show his respect. As for the rest of the tribespeople, only the younger, stronger manual laborers would get to eat meat, and even that meat would have to come from the animals that died in the blizzard.
For the young girls like Tsetseg, even though she was Hassan's daughter, she did not receive any preferential treatment.
It was also probably because of Hassan's impartiality that he became the tribe's chief.