I wrote a bit about the Eurasian steppe here.

While I won't say that my answer covers the entire history of pastoralism on the Eurasian steppe (it's mostly geared towards the 19th and early 20th century), I think it's nevertheless a useful starting point. The important takeaways are that: migration between different pastures was seasonal and cyclical, ie, families moved between commonly-recognized pastures every season, usually wintering in river valleys, moving upland in the spring, and then back down in the fall. While groups of people could pack up and move somewhere completely new, especially in times of crisis, that wasn't how things worked in an average year - you'd be mostly moving around in an established territory.