The easiest solution would be manually guarded gates. Open them in normal use, close them when centaurs are approaching. They don't interfere with normal usage so the people of the north can use carriages or ride horses.
But your question seems to strive for a technical solution. I assume that your centaurs are not wild animals with human-like features but intelligent creatures with horse bodies. Whatever technical solution you find you still need to guard and control it, as intelligent beings will find ways to work around or destroy it.
As the centaurs aren't horses I don't think that downward stairs are an obstacle for them like they may be for real horses.
The only way to differentiate between centaurs and humans is the size and mass of their body and their feet (hooves). So the two ideas I have are either a turnstile or a cattle grid.
A full height turnstile has to be build so that only single persons can pass it. The installation can be built in a massive fashion, like a very sturdy revolving door. It doesn't have to look like this modern example, more like a medieval revolving gate:
Other similar approaches are kissing gates or simple stiles. Those are generally inaccessible for livestock but may to easy to jump over when constructed in a way that they are still practical for humans.
Cattle grids generally work when they are long enough and animals can't jump over it. While they technically may work for your centaurs I think intelligent beings may find easy ways to circumvent these (e.g. with special snow-shoe style footwear).
I don't see any purely technical solution as viable against this kind of enemy. But you need to make life as hard as possible for the foe. So a combination of these measures (a guarded gate with cattle grid and probably revolving doors) may be the best solution.
Of course the rest of the wall needs to be unscalable for both people and centaurs. But even the real Great Wall wasn't just built for keeping invaders out but for keeping them trapped inside long enough when they were retreating so that the regular army could destroy them. With this in mind separating people from centaurs doesn't seem too important.