I'm not that familiar with SW Simulation, but from my experience with ANSYS, I would apply half the load. You are analyzing just half of the stool and the symmetry condition takes care of the influence of the other half.
A very simple way to check is to apply half of the load and then check the reactions at the feet. If I am right, they will add up to half of the load. The feet on the "other" half would be bearing the rest of the load.
Having said that, I would also model the full stool, because real loads are not necessarily going to be applied on the center line. As a person climbs up or down, they will put their full weight on one foot at a time.
Great idea regarding the reactions at the feet. Thanks!