Of course they weren't tied to the steppe. They could leave it. However, they needed to steppe to form these huge empires, and conquer settled cultures in the first place. This is due number of related reasons that are fundamentally about the unique steppe environment:
1) Large herds of horses consume monumental amounts of grass, especially when they are on the move during military campaigns. The steppe is suited for continuous occupation by these herds in a way that most of Europe or the ME isn't. The Mongol's forays into non-steppe areas were limited by available grass.
2) Related to this, abundant grass was why they had a horse-oriented culture and economy, and why horses were ridden by common people, and not just the elites - as in most all other areas.
3) While parts of Mongolia are mountainous and the Mongols and other steppe groups ventured into them, horses don't do well with very rugged terrain. Horses can't make it up many or most hiking trails in the American West, for example - they can't be too steep or have significant obstacles. In addition, again there is less grass in such areas.
To sum up, the Mongols and other riders needed the steppe for the abundant grass. The flatness of the Eurasian steppe also allowed for incredibly fast travel, which is why the Mongols, Turks, and others were able to have continuous cultures and empires from Europe to China.
Whenever the steppe conquerors conquered and ruled from non-steppe areas, they could not maintain massive cavalry (unless they were receiving reinforcements from the steppe). This leads to the treadmill of conquest and abandonment of the horse-oriented culture that made their conquests possible in the first place. That happened with the Iranians, Mongols, and various Turkic groups, among others.
You're missing my point here, which is that mountainous areas weren't some peripheral interstitial zone they would occasionally mount expeditions to with a lot of preparation and care. Rather, they were a core part of the Mongolian homeland and critical to the economic system of central asia. Mongolian horses were extremely important to that success, with good adaptations for the harsh environments and much better foraging than almost anyone else's. It allowed the Mongols to mount lightning fast campaigns across terrain no one else could, in conditions thought impossible. This was enabled by the incredible depth of experience with adverse, arid, and mountainous terrain possessed by Mongol commanders. If you want a specific example, look up the campaigns against Qara-Khitai, which famously included an expedition of ~30,000 over the Pamir mountains into Afghanistan in the dead of winter.
1) Large herds of horses consume monumental amounts of grass, especially when they are on the move during military campaigns. The steppe is suited for continuous occupation by these herds in a way that most of Europe or the ME isn't. The Mongol's forays into non-steppe areas were limited by available grass.
https://www.historynet.com/mongols-on-the-march-the-logistic...
2) Related to this, abundant grass was why they had a horse-oriented culture and economy, and why horses were ridden by common people, and not just the elites - as in most all other areas.
3) While parts of Mongolia are mountainous and the Mongols and other steppe groups ventured into them, horses don't do well with very rugged terrain. Horses can't make it up many or most hiking trails in the American West, for example - they can't be too steep or have significant obstacles. In addition, again there is less grass in such areas.
To sum up, the Mongols and other riders needed the steppe for the abundant grass. The flatness of the Eurasian steppe also allowed for incredibly fast travel, which is why the Mongols, Turks, and others were able to have continuous cultures and empires from Europe to China.
Whenever the steppe conquerors conquered and ruled from non-steppe areas, they could not maintain massive cavalry (unless they were receiving reinforcements from the steppe). This leads to the treadmill of conquest and abandonment of the horse-oriented culture that made their conquests possible in the first place. That happened with the Iranians, Mongols, and various Turkic groups, among others.