Generally, steppe armies couldn't walk all over Chinese armies. Chinese armies often won (one of the reasons why the Mongol conquest of China took decades). But steppe armies could and did win.

The three keys for a steppe army to beat a Chinese army were:

1. Tactical mobility

2. Operational mobility

3. Logistics and strategic mobility

The first two are largely about numbers. On the battlefield, all else being the same, it is better to have the larger army. However, the reach of the individual soldier is limited to either the length of his spear or the range of his crossbow or bow. The soldiers over there can't help over here. Cavalry have good battlefield mobility, and can concentrate at some point of the enemy line, and obtain a local superiority in numbers even if numerically inferior overall. If they can succeed in breaking through the enemy line at a weak point, they are well on the way to breaking the enemy formation and winning the battle. Their advantage in battlefield mobility results from two things: firstly, horses are fast, and secondly, infantry need to maintain formation for protection against cavalry.

There are various things that the infantry-based army can do to stop this from happening. These include fortifications (either field fortification or permanent fortifications, both used successfully by Chinese armies against steppe armies), having enough cavalry to counter the enemy cavalry (usually a goal of Chinese armies, even if not always successfully achieved), and having enough firepower - crossbows, bows, guns, and artillery - to keep the enemy cavalry away (often successfully used by Chinese armies). It isn't necessarily a case of foot archers using heavier bows and being more accurate - mounted archers could and did use very high draw weight bows, and could be accurate enough (especially at close range), and when every soldier in the steppe army is a mounted archer, the foot archers might be outnumbered. For a firepower advantage, range matters, and where Chinese armies used crossbows as a major weapon, these typically outranged bows.

Still, cavalry can cover distance quickly, and armoured cavalry can do so in the face of fire and close and engage crossbowen/archers in close combat, even if those same crossbowmen/archers could outshoot them if they stayed at range. Sustained fire, such as volley fire - continuous shooting by ranks - helps stop cavalry from closing. Also, infantry crossbowmen and archers can be protected by spearmen (or other infantry) and/or field fortifications. The English, with archer-heavy and cavalry-deficient armies in the Hundred Years War faced the same situation, and used armoured infantry and field fortifications to protect their archers (and if these weren't present, French armoured cavalry could and did close with and defeat the English archers).

Mobility off the battlefield matters, too. If you can move your armies faster, you can avoid battle with more powerful enemy armies, and fight weaker armies. This is Nathan Bedford Forrest's principle: "Get there first with the most men" (also a key to Wellington's success in Spain against the French). This was the key to Mongol success against the Jin. Their strategic planning was often mediocre, and, given equal numbers, Jin armies often performed well against the Mongols. However, the Mongols at the time had largely mastered the operational art of war, and fought when they had the advantage, and won more often than not.

Of course, avoiding battle can be impossible. Sometimes, the enemy must be stopped, or their army will capture the capital, a vital pass, devastate essential agricultural areas. Not having capitals or essential agricultural areas that must be defended at all costs helps a lot. If a Chinese army advanced into the steppe, the steppe army could withdraw, often at little cost. Combined with the ability of steppe armies to live off the steppe, and the dependence of Chinese armies advancing into the steppe on supplies carried with them or provided by a supply line, it was very difficult for a Chinese army to force a decisive battle on the steppe. If the steppe army could lure them far enough into the steppe, and then sever the supply line, starvation could do much of the work for them. These advantages didn't help much when the steppe army was invading China, so it is unsurprising to see that Chinese armies were much more successful when on the defensive against steppe armies than when on the offensive.