A majority of Eastern Woodland Tribes were not receptive of the horse. Reason being: travel in forests was not suited for horseback, hunting did not require a horse, and warfare would not benefit with a horse.

Travel: There were few if any prairies East of Appalachia. (It was often spoken that a squirrel could run from coast to coast and never touch the ground since the forests were so thick!) With so little clearings, travel between Native American villages and societies was limited to footpaths (Pequot Path through Connecticut, for example) and when possible, canoe travel. Since the networks were quite literally footpaths, horses would not fare well and their riders would be in a painful ride filled with branches and sticks as a consequence of their raised seat on horseback. Despite the conditions of these paths, it does not discount the interconnectivity of Eastern Woodlands people. Many of these footpaths have become modern right-of-ways of interstates and state highways!

Hunting: Consequently, hunting would not benefit from the horse. Large game like moose, deer, bear, and elk was done with quiet ambush-style bow and arrow and fishing was done weir-construction across stream channels. In a source I provided, a witness writes that a hunter could sneak up and kill a deer while it sleeps. These tactics required less energy to hunt and did not require having to provide care and feed for an animal used in the hunting process. Since northern sect of these peoples were semi-nomadic (Abenaki of northern New England, for example) and central and southern sects (Algonquin and Cherokee) only practiced small scale subsistence agriculture beyond hunting and gathering, the horse was never implemented as a draft animal.

Eastern Woodland warfare was, like hunting, ambush style and required speed and stealth. Horse were fast, but surely a warrior could not always hide one quietly with him and prepare for ambush.

By contrast, Plains People had a treeless plain that provided a different theatre for travel, hunting, and warfare.

A treeless plain provided easy travel, especially since horses evolved on a treeless plain and migrated from North American to the Asian Steppe some 10,000 years ago.

Hunting typically required extensive ambush tactics that was, if not dangerous, costly in energy. The horse allowed Plains People to abandon ambush tactics in favor of herding buffalo that ran well beyond the speed people can run at it. Maintenance for horses was simple on the plains too: horses grazed on the infinite bounty of grass (which in turn improved fertility of the soil).

Warfare, like the Eastern Woodlands people, was comprised of ambush style raids, but with horse, this gave an unprecedented advantage of speed.

The horse was simply better-suited for a prairie environment, and again, this is no wonder, when we consider horses evolved on the plains and migrated one...only to return thousands of years later.

Sources: National Geographic Encyclopedia on Native American Nations https://www.nps.gov/fora/learn/education/indian-fishing-and-hunting.htm