Until automobiles gave them the boot, horses were a totally essential part of nearly every human society, where they helped people with nearly every aspect of life. Take a look at this quote in which the TTC uses horses to symbolize two totally different states of affairs:
When the world has the Tao
Fast horses are retired to till the soil
When the world lacks the Tao
Warhorses give birth on the battlefield (46.1-4)
So horses were used to till the fields in peacetime and used to charge soldiers into battle in times of war. Here, the TTC uses the way horses were used to represent the overall state of society.
When everybody's living the peaceful life of the Tao, there's no need for horses to run; they can just plod along slowly, pulling a plow behind them (mmm, those lucky horses). Don't miss line 46.4 here, which gives us some of the most graphic imagery in the TTC. To us, a warhorse having to give birth amid the chaos of a battlefield is a perfect image to sum up the way the TTC says that war perverts the naturally peaceful ways of the Tao.
Horses aren't just used to represent peace and war in the TTC, though. Back in the day, having a horse was also a sign that you had some moolah. Check this quote:
Therefore, when crowning the Emperor
And installing the three ministers
Although there is the offering of jade before four horses
None of it can compare to being seated in this Tao (62-8.11)
So when a new Emperor was crowned, the Chinese would make an offering of the most valuable stuff they could lay their hands on: jade and horses. It says a lot about how much horses were worth that they'd be lumped in with something as valuable as jade, doesn't it?
Of course, the point here is that neither jade nor horses are worth diddly-squat compared to the great and eternal Tao. So these lines are ultimately using horses to symbolize the way that people put too much value on riches and possessions, when all they should really be focusing on is oneness with the Tao.