Horses have been around in China for thousands of years. Insofar as we can tell by recorded history, horse-drawn chariots played an important role in warfare starting in the second millennium B.C.E. The Chinese character for horse was created about that time, which first appeared on the animal bones used for divination (oracle bones) and then bronze vessels. The character, as it was drawn then, was basically a picture of a horse, something like this:
Around the time of the Han Dynasty (202 B.C.E.-220 AD), the word was written thus:
As the images above shows, the character took a more abstract form, but you still see the head, legs and tail of the horse. In the centuries that followed, the word was further simplified and standardized to look like this:
and finally like this:
As horses became more commonplace across China, their existence came to be reflected in the Chinese language more extensively. There came into being numerous expressions with references to "ma," horse. For example, to describe a situation where someone succeeds in tackling a task as soon as he arrives on the scene, or to express a wish for such a swift victory, there is the saying 马到成功 [mǎ dào chéng gōng] - “Success as soon as the horse reaches the destination." This is rather like the English expression that someone "rides to the rescue."
Flattery is a necessary part of any civilized society, even though most people probably would not say they're proud of it. One Chinese reference to such practice, with clear indication of disdain, is 拍马屁 [pāi mǎ pì] - "Pat the horse on its ass."
On a more positive note, the horse is commonly recognized and appreciated for its strength and stamina. 路遥知马力，日久见人心 [lù yáo zhī mǎ lì, rì jiǔ jiàn rén xīn] - ”On a long journey, you see the endurance of your horse; given time, you will see the true heart of a man."
Another Chinese saying about man's integrity that contains the word "horse" is 君子一言，驷马难追 [Jūn zǐ yī yán, sì mǎ nán zhuī] - "A gentleman's word goes so fast that even a chariot drawn by four horses cannot catch up with it." This is to say that a good man should keep his promises. Once he has said something and thus made a commitment, he should not try to go back on his word. As soon as you have said something, it's gone, it's out there in the world.
Horses run fast, and that's mostly a good thing. But sometimes you don't want your horses run so fast. In fact, sometimes you should not ride a horse at all. The Chinese frequently describe someone who is careless with the expression 走马观花 [zǒu mǎ guān huā] - "Looking at flowers in the field from atop a pacing horse." Someone like this is too casual and lofty to look at matters closely and attentively.