Magnetic metamaterials such as artificial spin ice offer a route to tailor magnetic properties. Such materials can be fabricated by lithographically defining arrays of nanoscale magnetic islands. The magnetostatic interactions between the elements are influenced by their shape and geometric arrangement and can lead to long-range ordering. We demonstrate how the magnetic order in a two-dimensional periodic array of circular disks is controlled by the lattice symmetry. Antiferromagnetic and ferromagnetic order extending through the entire array is observed for the square and hexagonal lattice, respectively. Furthermore, we show that a minute deviation from perfect circularity of the elements along a preferred direction results in room-temperature blocking and favors collinear spin textures