History of Horse World 1000 BC - 300 BC. Early Classical Era.
Old World:
Mycenae finally fell to the Dacian onslaught, however eventually, the local Dacians were assimilated by the remnants of Mycenean culture to create the Pyriote Confederation unifying Greece Proper, how ever loosely. Troy became a leading power in the east, gaining control over East Cyprus, Crete and the Aegean. Syracuse was abandoned. Karthavea was slowly, but surely expanding and making good use of agriculture. In Middle East, the camels dominated the battlefield. Hyksos camel-riders defeated Arameans and went with sword and fire throughout much of Phoenicea until it was stopped at Haifa. This opened the path to Sidon unifying the Phoeniceans (as all others were even more crippled), though the area in Anatolia was lost to Abrahamea, which in the same time begun developping the Old World's first monotheism. Sidonese Phoenicea soon restarted naval expansion, rebuilding Syracuse (Siraks-Hadasha, or just Siraks) and establishing trade posts on African and Italian coasts. Arameans, expelled from their lands by the Hyksos proceeded to destroy the kingdom of their assimilated relatives in Sumeria. Many Sumerian achievements were lost to that invasion... Egypt was the only trully-prospering Old World civilization. It too utilized the camels well under the "Expansionist Dynasty" of Pharaohs such as Ptahotep, Nekhekre, Amenhotep (

) and Mahoseph (this period was in circa 800 BC - 500 BC), crushing and enslaving the Nubians and the Libyans (in Cyrenaica). Dravidia was stagnating. Longshanese China eventually collapsed, but much like a Phoenix, it rose again as the Wang-li Empire, gaining the tradition of chronology which was of much use to historians later on and having somewhat expanded further south, while developping a road system and a "runner" message system to go along with it, providing fairly efficient buerocracy.
New World (as usual, in more detail then Old World as it is more interesting and "better-known" to historians of Horse World):
Great Lakes: circa 900 BC, near OTL Lake Erie, fortified settlements of a bronze-age culture of Vaahna emerged. It is interesting as it was a fully-fledged civilization despite being thought of as "barbarians". It acknowledged the power of a Mahnadrin (Supreme Ruler, king), had a developed runic alphabet and some primitive agriculture (including some sort of a cow-like mammal which evolved from a bison. And this is not the last that you will hear from evolution of species in this TL!). The Vaahna have used the southward migration of Hodenaans to move west, fighting the remaining Hodenaans and claiming new lands (controlling much of the area south of the Great Lakes), something that was forever remembered in "Ohaalarinod", "Tale of Aalarini".
Messipia: As of 1000 BC, Messipia was at its zenith, perhaps, as it had been the first civilization to fully use the potential of the "baws" (bison cows) to help its agriculture and to use bronze weapons. Circa 850 BC, the 5th Dynasty Messipians conquered Ereniji. That proved their undoing, though, as the war tired them and brought them in direct confrontation with the Hodenaans at the time of a particularily harsh winter. Naturally, the Hodenaans begun moving south en masse as soon as they heard that the Messipian army had troubles asserting control over new areas. Tragically, Messipia was crushed, but luckily, the more important of its achievements survived, allowing the Hodenaans who settled on the coast to start everything anew. The Haellian Empire that rose on the ruins of Messipia was even greater. In circa 550 BC, as Iron Age reached Messipia, the other Hodenaans in the area were subjugated, and expansion was taking place, primarily east-wards. There was occasional maritime contact with the rising civilizations of Mesoamerica, although it was also from the south that the main threat to Haellian Messipia came - Carib raiders, having developped advanced boats (think protolongboats) were devastating the coastline and the trade ports.
California (OOC: read: pretty much all of North America's Pacific coast): Around that time, the Orasezi peoples were settling down in the four main "city valleys" of California: the southern or Sasezi (in Sonora), southern-middle or Velezi (around Los Angeles), northern-middle or Mareli (around San Francisco) and northern or Irenezi (Seattle-Vancouver). By 700 BC, there were pretty much well-established unified and urbanized states in each valley, sharing a language and general traits of the culture. The interesting part about the Orasezi culture was that it was a very philosophical one, but rather then become a mystical, religious culture like the Mayans and the Hamese, the Orasezi culture was increasingly based on "rationality". It was in it that advanced mathematics, logic and (by a side effect) advanced architecture emerged. The religion was a typical tolerant polytheism. The four valleys were isolated from the rest of the New World at first, and traded (and occasionally fought) with each other. Naval warfare gained importance there as well, as it was hard to travel through the hills and the deserts between the valleys.
Mekhikia: Back in Mesoamerica, circa 900 BC the Olmec state mystiriously disappeared. It is believed that it either collapsed by itself, either due to the Carib raids and/or the Mekhikian pressure. The Mekhikians took some parts of the Olmec culture, but large amount of cultural influence came from the Mayans. As a result, the Mekhikians formed their own states, largely based on tribal despotism evolving into kingship. After several wars with large use of chariots and occasional Mayan intervention, in circa 700 BC the Mekhikians formed the empire of Kharek. It was during the Mekhikian Wars that Iron Age had begun.
Mayans: Tikalese Empire was weakened by volcanic explosions near its center, and after the death of Palenhoe in 831 BC, the Mayans were redivided. The northern city states, forming the Chichen Itza League, conquered numerous northern territory, but descendants of the Tikalese ruling dynasty relocated their capital to Aruizotl on the Pacific coast. The wetlands and jungles of "Petan", the area where Tikal was originally located, became the border between the two Mayan powers. Both developped well, especially in fields of astrology and architecture but also developping advanced alphabeths and sailing ships ("Quetza" galleys). While Chichen Itza used its naval technology to set up a somewhat usable (though still dangerous due to the Carib raids) trade route to Messipia, Aruizotlese "Quetzas" sailed south, establishing trade contacts with local peoples. Eventually, this brought them into contact with the Moche peoples (667 BC), stimulating development in the Andes...
The Andes: At that point, Chavin and Paraca were the dominant powers in the region. However, the establishment of contact with the Mayans was the privilege of the then-minor Moche peoples. Having acquired from the trade secrets of bronze working, the Moche soon became an important power as well. The three powers were rarely fighting seriously, though, as they were too distant from each other.
Argentina: Previous dominated by local horse nomads (the Orese), it was in about 700 BC that the Hamese people have arrived, presumably from the Andes. The Hamese settled in the Pampas, and soon became a distinct cultural entity. They worshipped a single god, Haanar (The Eternal Wind), and were ran by a theocratic ruler. The Hamese, having founded the city of Haa-Phel, used advanced cavalry (with stirrups and reins) against the Orese (who presumably were looting their temples), pushing them out to the harsh(er) lands of Patagonia.