Magnetic artificial spin ice provides examples of how competing interactions between magnetic nanoelements can lead to a range of fascinating and unusual phenomena. We examine theoretically a class of spin ice tilings, called pinwheel, for which near degeneracy of spin configuration energies can be achieved. The pinwheel tiling is a simple but crucial variant on the square ice geometry, in which each nanoelement of square ice is rotated some angle about its midpoint. Surprisingly, this rotation leads to an intriguing phase transition; and even though the spins are not parallel to one another, a ferromagnetic phase is found for rotation angles near 45∘. Here, magnetic domains and domain walls are found when viewed in terms of net magnetisation. Moreover, the ferromagnetic behaviour of the system depends on its anisotropy which we can control by array shape and size.