The horses travelled as a herd, and like most herding animals tended to stick together. Moreover, they were very well-trained and have even been referred to as "dog-like" in their coming at the beck-and-call of their human masters. Yes, they'd be tied off when not on the move or if it was thought that they might be needed quickly, but especially when not actively on campaign, they could be let out to pasture to take care of themselves until dusk when they'd be rounded up and taken back to camp for their own protection against wolves.

Your question seems to imply that you thinking taking such a "host" would have increased the burden for a Mongol party on the move. In fact, it was much the opposite. The horses themselves greatly increased the range and efficiency of the Mongol riding them, while at the same time vastly lightening the load needed to "train" behind them. Horses we not just vehicles, but also served as a primary dietary source for their riders. Now, of course you would not want to kill and eat your mount(s) unless in the most dire of circumstances, but mare's milk was one of the major nutritional inputs for Mongols on the move. In case of need of a little additional protein, one of the horse's veins could be lanced and a bit of their blood mixed in with it. Any game meat could likewise be "cooked" on the go by sticking it underneath the rider's saddle and allowing the friction and the body-heat from the day's ride to render fit for consumption.

The beauty of this system was that, so long as the Mongol force moved primarily over the Asian steppelands, they didn't need to worry about bringing sufficient fodder for their many mounts. The grasslands surrounding them took care of virtually all of the mares' dietary needs.

I'm not sure where you're getting the idea that entire families went off on campaign. That as not the case, and indeed why steppe women in general were so well-trained in the skills of the horse and bow themselves. For nomads generally, and the steppe-riders in particular, having women be "dainty, pretty things" without real-world skills was simply out of the question. While the men were away (either on a hunt, or on a war campaign) the women would remain behind with the cattle herds and the children, and were in charge of the ger, of financial decisions, and of society as a whole. Thus they needed to be able to defend their possessions and themselves from those who might come across them with the majority of males of fighting age far off - be that threat animal or human. Female equanimity in society didn't go away when the men returned, either. Men were not in charge of financial decisions, nor did they have free reign over the women or their private gers. They needed permission to enter, and had to abide by very strict and ritualized codes of conduct when around women even of their own family.

What I think you might be getting at is the idea that there was not "separate military corps" set apart from civilian life. All men were expected to take part in hunts and military excursions at the behest of their khan.

Anyways, back to the horses. Why travel with so many mounts? Easy - it made them much faster and able to cover far longer distances. Horses, of courses, get tired after being ridden for a time - even the trusy, sturdy Mongolian horses. But by having sufficiently extra mounts, a rider could simply "swap out" for another of his mares (and yes, I keep saying mares, since the females were the only ones ridden, since they produced - yep - milk) and keep going, while the tired horse could fall back and take a break, eat some grass, and catch back up later. The rider could therefore continue without stopping, for days on end if necessary... a feat that absolutely confounded agrarian societies, and caused many of them to vastly overestimate the actual number of Mongol cavalry they were facing in an engagement.

This also served the Mongols well in combat with settled societies - especially those that could be tricked by one their favorite tactics: the "feigned flight." Cavalry would charge at an enemy position, only to break off and seemingly ride away in panic at top speed. This often prompted the enemy cavalry force to attempt to ride the fleeing Mongols down and finish the job. Unbeknownst to them, however, the Mongol riders were riding toward another of their mounts that had been pre-positioned far off, such that by the time the warrior and and pursuers reached it, both of their horses would be ready to spit the bit. But whereas the Mongol warrior could simply swap over to his fresh and waiting mount (along with a fully stocked new quiver of arrows), his pursuers were now miles away from their own lines and on a dead-tired mount - in other words, a sitting duck.

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Allsen, Thomas. "The Rise of the Mongolian Empire and Mongol Rule in North China" in The Cambridge History of China, Vol. 6: Alien Regimes and Border States.

Hildinger, Erik. Warriors of the Steppe: A Military History of Central Asia, 500 B.C. to A.D. 1700

Weatherford, Jack. Genghis Khan and the Making of the Modern World.