The average horse eats 10-20 pounds per day, according to this pet website. Considering the fact that the horses may have to eat even more because of the hard traveling they had to endure, it's likely that food costs must have been incredible. Genghis Khan's army traveled an average of 14 miles (23 km) a day during the China campaigns, with some claiming they traveled 120 miles per day when 'charging towards a target'. In addition, each horseman kept 3-4 horses in tow.
Let's do the math: 100,000 mounted archers * 4 horses each * 10 kg/day * 250 days/campaign = 1,000,000,000 kg of forage required each campaign.
As noted here annual forage yield of meadow steppe is about 2000 kg/ha; of typical steppe about 900 kg/ha; and even desert steppe yields 200 kg/ha. Thus the area required to support Genghis's cavalry for a campaign ranges between 500,000 to 1,000,000 ha, or 5,000 to 10,000 km^2. A single day's forage could be found in an area of 20 to 40 km^2, which seems quite a reasonable campground size for an army of 100,000 cavalrymen.
Of course, given this forage requirement, it is no surprise that Genghis's army moved so rapidly - if it didn't it was going to starve.
Update: Genghis's army rode ponies, not full horses, reducing forage needs accordingly.
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Of course "thread" will cover much more area than "group". That means more steppe to feed horses. Let's say length of the army is 50km, and horses can go 2 km at most from the line to eat. Then it would cover 100km^2, and if army marches 23km a day, it would be 46km^2. Still sufficient. On the other hand, if they move in a dense group like rectangular then horse feeding is going to be problem as there are too many horses in less space. Also sparse much bigger rectangular group may lead to too much dust and soil devastation. So marching like "thread" is enforcement. Genghis Khan's army was full of cavalries. If there was more infantry like other nations, horses won't have problem of feeding in rectangular group.
Also Mongolian horse is kind of wild, it doesn't require much care like other horses(http://en.wikipedia.org/wiki/Mongolian_horse).
In Vasily Yan's "Bat khan" book, the army's maneuver explained in detail. Bat is grandson of Genghis Khan, apprentice of general Subotai. You may use the book as starting point to further investigation. Here's the google search results http://bit.ly/NSGCTt, book on Amazon http://amzn.to/1fFTiJD
I written quiet long post that doesn't fit in comment section, so dropped in answers.
This is not really an answer to your question, but the following numbers look much more realistic.
According to Dmitriy Chernyshevsky, Zhaksylyk Sabitov ("Questions of History and Archaeology of Western Kazakhstan")