Artificial arrays of interacting magnetic elements provide an uncharted arena in which the physics of magnetic frustration and magnetic monopoles can be observed in real space and in real time. These systems offer the formidable opportunity to investigate a wide range of collective magnetic phenomena with a lab-on-chip approach and to explore various theoretical predictions from spin models. Here, we study artificial square ice systems numerically and use micromagnetic simulations to understand how the geometrical parameters of the individual magnetic elements affect the energy levels of an isolated square vertex. More specifically, we address the question of whether the celebrated square ice model could be made relevant for artificial square ice systems. Our work reveals that tuning the geometry alone should not allow the experimental realization of the square ice model when using nanomagnets coupled through the magnetostatic interaction. However, low-aspect ratios combined with small gaps separating neighboring magnetic elements of moderated thickness might permit approaching the ideal case where the degeneracy of the ice rule states is recovered.