Exploiting current-induced spin-orbit torques (SOTs) to manipulate the magnetic state of dipolar-coupled nanomagnet systems with in-plane magnetic anisotropy, such as artificial spin ices, provides a route to local, electrically programmable control of the magnetization, with relevance for applications including neuromorphic computing and reconfigurable magnonics. Here, we demonstrate how the orientation of a nanomagnet relative to the direction of an applied electrical current impacts the threshold current density needed for all-electrical field-free magnetization switching, and how dipolar coupling between the nanomagnets influences the switching of interacting pairs and ensembles of nanomagnets. Using a material system designed to generate SOTs in response to electrical currents, we find that the current required to switch the magnetization of isolated nanomagnets varies nonmonotonically as the angle between the nanomagnet long axis and the current increases. This trend in the switching current is also seen in pairs of nanomagnets. These nanomagnet pairs can switch either sequentially or simultaneously, depending on their relative geometry (side-by-side or end-to-end) and the applied current density. In small artificial spin ices, we observe a similar angular dependence of the switching current, which can be used to control the magnetization orientation of specific subsets of nanomagnets. The experimental results are supported by micromagnetic modeling, which illustrates how the various current-induced torques can be exploited to control the magnetization switching. This work thus establishes SOT switching as a practical mechanism for programmable manipulation of dipolar-coupled nanomagnetic systems.