We have studied the temperature and magnetic field dependence of the total magnetic moment of large-area permalloy artificial square spin ice arrays. The temperature dependence and hysteresis behavior are consistent with the coherent magnetization reversal expected in the Stoner-Wohlfarth model, with clear deviations due to inter-island interactions at small lattice spacing. Through micromagnetic simulations, we explore this behavior and demonstrate that the deviations result from increasingly complex magnetization reversal at small lattice spacing, induced by inter-island interactions, and depending critically on details of the island shapes. These results establish new means to tune the physical properties of artificial spin ice structures and other interacting nanomagnet systems, such as patterned magnetic media.