What if the horse had never existed?

Today, horses are considered something of an anachronism, hearkening back to a time when they represented the most important mode of transportation known to man, for a period of thousands of years. Today, horses are merely very expensive pets of the rich, a form of rather dangerous entertainment for those who have nothing else to do with their time and money. But, in the past, horses were a terrific symbol of power and freedom, a means of quadrupling speed for transport of all types. They were essential for transportation, farming, industry, commerce and warfare. They formed the basis for the development of all important civilizations and societies throughout Europe, Asia and Africa. However, in North America, horses went extinct over ten thousand years ago. They were only reintroduced by European colonists, particularly the Spaniards, in the sixteenth century. There are two important and interesting coincidences here. First of all, the wheel was invented just about the same time that horses became domesticated in Europe, Asia and Mesopotamia. Secondly, the wheel was never invented at all in the Western Hemisphere, at least for any practical applications, where horses did not exist, because they had become extinct in paleolithic times. So, it appears possible, that the horse is actually an essential reason for the invention of the wheel, because without the horse, there is nothing strong enough and fast enough to pull vehicles on wheels, at high speed, for any significant distance. In other words, no horses, no wheels. And, without wheels, virtually all mechanisms of industrial society cease to exist. So, no horses, no wheels, no modern civilization. We're effectively stuck at the level of the Aztecs and the Incas. Thoughts?