I would expect them to be a hunter gatherer society.

Think about it. They would have a hell of a time with agriculture. There would be no end to the problems with planting and I think they would have serious moral issues with keeping horses or bovine.

I think that the majority of their hunting would be done as a speed and pack hunting manner. Think more wolves, less cheetah.

Gathering would still be the large majority of the caloric intake. Having an equine digestive system at the end of their human digestive system would be that they can get along with a lot of grasses.

This means that nomadic lifestyle necessity. They use speed and herd movement as the major forms of defense thanks to the equine lower parts. So the nomadic stuff makes even more sense. It also seems that they wouldn't get much beyond the equatorial regions, maybe in some temperate plains and grass lands, but only as far as they can range before winter.

With the nomadic lifestyle and wide ranging there ends up being spoken language so that knowledge gets passed beyond a generation, this means the ranging can grow again.

Those arms and hands though....I don't know if they ever get to tools unless they are part of raid warfare. They definitely don't get them as a part of their own culture. Think about it. They have those six pack abs because of how hard it is to get the human half close enough to the ground to feed. I can't imagine them spending a long time doubled over to smash rocks against one another to get to rudimentary tools. This means that things like the trade gets centered around slaves, since the centaurs can physically overcome humans and other great apes with ease. So we basically end up with the equatorial regions of Africa, the Middle East, Asia and Europe harried by slaver centaurs.

The centaurs are kept in check by wily humans that develop advanced technology. But the herds occasionally move through and take human slaves and sell them back. The advent of pikes and bows escalates the wars between humans and centaurs. Eventually civilization triumphs and pushes the centaurs to extremely remote pockets across the globe. They aren't dead, but live on the centaur reserves is a cruel reminder of the cost of survival.

Now their society is non-functional. Everything that it was based on is gone as the ranges are strangled. The oral mysticism is crushed by human education. The century of s system of shitty government "protection" has turned most of their proud species to being reliant on government hand outs. They didn't understand the terms of the peace they bartered, but now they can't even function in it. Their youth are disenfranchised. The future seems hopeless...

So to bring it back.

Nomadic, with advanced language skills, historicity and oral culture. Confined to the equator or the range of the herd(?) within the summer season. Eventually they gather technology through raiding and slave trade. But technology eventually out distances physical might and the culture gets dominated by humans. So today they are essentially the same as aboriginals throughout the world.

At least Canada officially apologized recently. Sorry for what my ancestors did to your ancestors. Sorry that we keep failing. Sorry that we can't even vote to help you anymore...sorry native Canadians.